## Issue 1Volume 7 (2019)

 Authors : D. Senthilkumar and P. Tamil Selvi Title : Weighted Composition of m-Quasi k-Paranormal Operators Volume, Issue, Year : 7(1)(2019) Pages : 1−8

Abstract: In this paper we discuss the conditions for a composition operator and a weighted composition operator to be m-quasi k-paranormal operator and also the characterization of m-quasi k-paranormal operator on weighted Hardy space.

Keywords: m-quasi k-paranormal operator,Composition operator,Weighted Hardy space.

 Authors : Khawlah Hashim Hussain Title : Some New Modifications of Adomian Technique for Nonlinear Volterra Integral Equations Volume, Issue, Year : 7(1)(2019) Pages : 9−14

Abstract: In this paper, the nonlinear Volterra integral equations are solved by using new modifications of the Adomian decomposition technique. The approximate solution of this equation is calculated in the form of a series with easily computable components. The accuracy of the proposed techniques are examined by comparison with exact results. The test problems are presented to illustrate the reliability and performance of the techniques.

Keywords: Adomian decomposition technique, Laplace transform, Nonlinear Volterra integral equation.

 Authors : Aakansha Vyas and P. K. Mishra Title : Fractional Differential Operator of Generalized Mittag-Leffler Function Using Jacobi Polynomial Volume, Issue, Year : 7(1)(2019) Pages : 15−22

Abstract: The paper is devoted to the study of generalized fractional calculus of the generalized Mittag-Leffler function $E^{\delta } _{\upsilon ,\rho } \left(z\right)$ which is an entire function of the form $E^{\delta } _{\upsilon ,\rho } \left(z\right)=\sum\limits_{s=0}^{\infty } \frac{\left(\delta \right)_{s} z^{s} }{{\rm \Gamma }\left(\upsilon s+\rho \right)\; s!}$ Where $\upsilon >0$ and $\rho >0$. For $\delta =1$, it is reduces to Mittag-Leffler function $E_{\upsilon ,\rho } \left(z\right)$. We have shown that the generalized fractional calculus operators transform such function with power multipliers in to generalized Wright function. Some elegant results obtained by Kilbas and Saigo [11], Saxena and Saigo [24] are the special cases of the result derived in this paper.

Keywords: Generalized Mittag-Leffler function, Generalized Fractional Calculus, Generalized Wright function, Jacoby Polynomial.

 Authors : S. M. Vanithalakshmi, S. K. Narasimhamurthy and M. K. Roopa Title : On $\mathbb{R}$-Complex Finsler Space with Matsumoto Metric Volume, Issue, Year : 7(1)(2019) Pages : 23−30

Abstract: In this paper, we determined the fundemental tensor fields $( \tilde g_{ij}, \tilde g_{i\bar j})$ and inverse of these tensor fields, their determinant. Further, we studied some properties of non-Hermitian $\mathbb{R}$-complex Finsler space with Matsumoto metric.

Keywords: $\mathbb{R}$-Complex Finsler space, $\mathbb{R}$-complex Finsler space with $(\alpha,\beta)$ metics, $\mathbb{R}$-complex Finsler space with Matsumoto metric.

 Authors : T. Elbouayachi Title : Chirps Construct on Sobolev Spaces and the Behavior of their ${\left\|\hspace{.5cm}\right\|}_{L^2[-\varepsilon,\varepsilon]}$ and ${\left\|\hspace{.5cm}\right\|}_{H^s[-\varepsilon ,\varepsilon ]}$ Norm Volume, Issue, Year : 7(1)(2019) Pages : 31−39

Abstract: The main idea of this work is to characterize chirps construct on Sobolev spaces by studying the behavior of ${\left\|f\right\|}_{L^2[-\varepsilon ,\varepsilon ]}$ or ${\left\|f\right\|}_{H^s[-\varepsilon ,\varepsilon ]}$. We expect that the behavior is in order of ${\varepsilon }^{\alpha +\left(\beta +1\right)(\left|s\right|+\frac{1}{2})}$ when $s$ tend to $-\infty$, and we believe that we have equivalence between this and the definition of chirps construct on Sobolev spaces. The formula of a chirp is given in the form ${f\left(x\right)=\left|x\right|}^{\alpha }g({\left|x\right|}^{-\beta })$, where $\beta >0$ and $g$ is an indefinitely oscillating function on $L^2$ or $H^s$. Which means that $g$ has for all $m$ integer one primitive of the order $m$ in the same space.

Keywords: Sobolev Spaces, Norm, Behavior of ${\left\|f\right\|}_{L^2[-\varepsilon ,\varepsilon ]}$.

 Authors : Jula Kabeto Bunkure Title : Lebegue-Bochner Spaces and Evolution Triples Volume, Issue, Year : 7(1)(2019) Pages : 41−52

Abstract: The functional-analytic approach to the solution of partial differential equations requires knowledge of the properties of spaces of functions of one or several real variables. A large class of infinite dimensional dynamical systems (evolution systems) can be modeled as an abstract differential equation defined on a suitable Banach space or on a suitable manifold therein. The advantage of such an abstract formulation lies not only on its generality but also in the insight that can be gained about the many common unifying properties that tie together apparently diverse problems. It is clear that such a study relies on the knowledge of various spaces of vector valued functions (i.e., of Banach space valued functions). For this reason some facts about vector valued functions is introduced. We introduce the various notions of measurability for such functions and then based on them we define the different integrals corresponding to them. A function $f:\Omega \to X$ is strongly measurable if and only if it is the uniform limit almost everywhere of a sequence of countable-valued, $\Sigma$-measurable functions. If X is separable and $f: \Omega\to X$, be a function then the following three properties are equivalent: (a) f is strongly measurable; (b) f is weakly measurable; (c) f is Borel measurable. A strongly measurable function $f: \Omega\to X$, is Bochner integrable if and only if the function $\omega\to \left\|f\left(\omega \right)\right\|_X$ is Lebesgue integrable (i.e., $\left\|f\left(.\right)\right\|_X\in L^{1}(\Omega)$). The emphasis of the project is on the so-called Bochner integral, which generalizes in a very natural way the classical Lebesgue integral to vector valued functions. We continue with vector valued functions and introduce the so-called Lebesgue-Bochner spaces, which extend to vector valued functions of the well known Lebesgue $L^{p}$-spaces. We also consider evolution triples and the function spaces associated with them. Evolution triples provide a suitable analytical framework for the study of a large class of linear and nonlinear evolution equations.

Keywords: Banach space, nonlinear, Lebesgue-Bochner, evolution triples.

 Authors : H. M. Fenta, P. Kibebew, S. T. Nigatu, Z. Siraye and A. Mulu Title : Status of Employment in Ethiopia: Bahir Dar University Graduates Tracer Study Volume, Issue, Year : 7(1)(2019) Pages : 53−58

Abstract: Background: Both graduates and Higher Education Institutions are increasingly concerned with ensuring that their academic investment results in future employability. The FDRE Ministry of Education has targeted to reach $>$ 80\% of graduates with the first degree of the regular program employed with degree-relevant employment within 1 year after their graduation. Therefore, this GTS was carried out to explore the employability rate, the average time it takes a graduate to find employment measured in months and assess if the employed graduates were employed in their field of study of 2015 and 2016 Bahir Dar University graduates with a first degree, in general.
Method: The study was conducted in Bahir Dar University in 2015 and 2016 regular, first-degree graduates and stratified multistage random sampling was used to select respondents. Out of 4208 graduates, 867 graduates with a response rate of 82.5\% were selected to participate in the study. To determine the prevalence, the duration and the potential factors of employability graduates' in the labor market, both descriptive and inferential statistics were applied.
Result: Seventy-nine percent of surveyed graduates were gainfully employed, of which majority (93\%) was landing with degree-relevant jobs. Most of the employment rate was taking place during 1 to 6 months in duration and the overall average duration of unemployment was 5.08 months. Moreover, the graduates from the Institute of textile and fashion technology and College of Business and Economics have a shorter spell of unemployment (3.62 and 4.41 months) respectively.

Keywords: Employability rate, degree-relevant job, Unemployment Duration.

 Authors : Sanaa Al-Marzouki Title : A New Generalization of Power Lomax Distribution Volume, Issue, Year : 7(1)(2019) Pages : 59−68

Abstract: A new generalization of the power Lomax (PL) distribution, called exponentiated power Lomax (EPL), is introduced for modeling lifetime data. Some statistical properties of the EPL distribution are provided. Explicit expressions for the quntile, moments, moment generating function, probability weighted moments and order statistics are studied. Maximum likelihood estimation technique is employed to estimate the model parameters are presented. In addition, the superiority of the EPL distribution is illustrated with applications to two real data sets.

Keywords: Exponentiated-G family; Power Lomax distribution, Order statistics; moments.

 Authors : Jula Kabeto Bunkure and Shimelis Adugna Tesema Title : Assessing the Impact of Implementation of Higher Diploma Program in Ethiopian Institute of Textile and Fashion Technology(EiTEX) Volume, Issue, Year : 7(1)(2019) Pages : 69−83

Abstract: This article determine the Higher Diploma program trained and no-trained teachers' skills in classroom instruction as well as pinning to the possible bottlenecks that hamper the successful application of the training skills. On this research a descriptive survey research design and explanatory research method where both qualitative and quantitative data gathering methods and analysis were used. The participants of the study were 20 HDP trained and 20 non-HDP trained teachers and 12 teachers on focused group discussion. The tools for collecting data or gathering data were: Questionnaire, classroom observation and Focused Group Discussion(FGD). In analyzing the quantitative data, statistical techniques of percentage, frequency count, mean and standard deviation were employed. The results indicate that HDP trained teachers were found to be better at reflective practice, implementing variety of active learning methods and assessment techniques than that of non HDP trained ones. However, both HDP trained and non HDP trained teachers have similar attitude towards the use of active learning methods and assessment techniques in their classrooms and it was found to be positive, since HDP trained teachers were found to be better at reflective practice, implementing variety of active learning methods and assessment techniques than that of non HDP trained ones. Besides, independent sample t-test and chi-square were used. The data gathered through qualitative methods was categorized and analyzed on thematic basis as raised in the objectives and the research questions. Large class size, classroom arrangement, lack of resources, and students' passive involvement were mentioned as major challenges to the implementation of a range of active learning methods and assessment techniques. Thus, the university should strengthen the HDP training to promote reflective practice, implementation of active learning methods and use of assessment techniques.

Keywords: Implementation, Skills,active learning methods and assessment techniques.

 Authors : Sanaa Al-Marzouki and Taghreed Al-Said Title : Truncated Weibull Lomax Distribution and its Statistical Inference Volume, Issue, Year : 7(1)(2019) Pages : 85−92

Abstract: A new three-parameter lifetime model, called the Truncated Weibull Lomax (TWL) distribution, is introduced. We investigate the density (pdf), distribution function (cdf), survival function (sf), hazard function (hrf), quantile function, r\textsuperscript{th} moment, incomplete moments and order statistics. Maximum Likelihood methods to estimate the TWL distribution parameters are studied. One real data set is applied to illustrate the flexibility of the TWL model compared with some Known models.

Keywords: Lomax distribution, Truncated Weibull-G family, Moments, Maximum likelihood estimation.

 Authors : Jula Kabeto Bunkure and Shimelis Adugna Tesema Title : Determining the impact of Higher Diploma Program on the education Quality: The case of Ethiopian institute of Textile and Fashion Technology(EiTEX) Volume, Issue, Year : 7(1)(2019) Pages : 93−106

Abstract: The objective of this study was to Determining the impact of Being thought by Higher Diploma Program trained teacher and Non Higher Diploma Program(HdP) trained teacher on the education Quality. Multiple instruments with multiple sources were used in data collection in the following order: Questionnaire, classroom observation, and Focused group duscussion.On this research qualitative and quantitative data gathering methods and analysis were used. The participants of the study were 331 students from different department and different batch, 20 HDP trained and 20 non-HDP trained teachers. The results indicate that HDP trained teachers were found to be better impact on improving education quality than that of non HDP trained ones. Besides, independent sample t-test and chi square were used. The data gathered through qualitative methods was Large class size, classroom arrangement, lack of resources, and students' passive involvement were mentioned as major challenges to the implementation of a range of active learning methods ad assessment techniques. Thus, the university should strengthen the HDP training to promote Education quality.

Keywords: Impact, qualitative,active learning methods, Quality.

 Authors : Saeed M. Ali Title : Classification of a Nonlinear Fin Equation in Spherical Coordinates via Lie Symmetry Method Volume, Issue, Year : 7(1)(2019) Pages : 107−120

Abstract: The nonlinear fin equation in Spherical coordinates is studied in this paper. Classification of temperature dependent thermal conductivity and radial variable heat transfer coefficient is performed via Lie symmetry analysis. Using these symmetries, nonlinear fin equation in spherical coordinates has been transformed into an ordinary differential equation. An Exact solution of this ODE is obtained whenever possible.

Keywords: Lie Symmetry Analysis, Fin Equation, Exact Solutions.

 Authors : Rachid El Jid Title : MLS Method: Numerical Error and Solution of a Unilateral Contact Problem Using Penalty and Lagrange Multiplier Volume, Issue, Year : 7(1)(2019) Pages : 121−136

Abstract: In this paper we propose a meshless approach (MLS) to solve two-dimensional unilateral contact problems. The convergence error of this method is studied, the element free Galerkin method and Galerkin formulation for two dimensional elasticity problems are considered. Then, the penalization method for the imposition of a contact constraint is proposed and the Lagrange multiplier method is used to impose essential boundary conditions. The implementation of the penalty / lagrange multiplier algorithm is described and the efficiency of our algorithm is illustrated by various examples.

Keywords: Meshless Method, Moving Least Squares, Cnvergence error, Contact problem, Variational inequality, Penalty method, Lagrange multiplier method, Numerical experiment.

 Authors : P. Anuradha Kameswari, S. B. T. Sundari Katakam Title : Implementing Wiener's Extensions in the Range $N^\frac{1}{4}\leq d$ < $N^{\frac{3}{4}-\beta}$ and $N^{\frac{1}{4}}\leq d$ < $N^{(\frac{1-\gamma}{2})}$, $\gamma\leq\frac{1}{2}$ with Lattice Reduction Volume, Issue, Year : 7(1)(2019) Pages : 137−148

Abstract: In this paper, Wiener Attack extensions on RSA are implemented with approximation via lattice reduction. The continued fraction based arguments of Wiener Attack extensions in the range $N^\frac{1}{4}\leq d$ < $N^{\frac{3}{4}-\beta}$, $p-q=N^{\beta}$ and $N^{\frac{1}{4}}\leq d$ < $N^{(\frac{1-\gamma}{2})}$, $|\rho q - p|\leq \frac{N^{\gamma}}{16}$, $1 \leq \rho \leq 2$, $\gamma\leq\frac{1}{2}$, are implemented with the Lattice based arguments and the LLL algorithm is used for reducing a basis of a lattice.

Keywords: Lattice reduction, LLL algorithm, quadratic form, Wiener Attack extensions.

 Authors : Prashantha Rao and Shashirekha B Rai Title : Convex and Weakly Convex Subsets of a Pseudo Ordered Set Volume, Issue, Year : 7(1)(2019) Pages : 149−154

Abstract: In this paper the notion of convex and weakly convex (w-convex) subsets of a pseudo ordered set is introduced and several characterizations are proved. It is proved that set of all convex subsets of a pseudo ordered set $A$ forms a complete lattice. Notion of isomorphism of psosets is introduced and characterization for convex isomorphic psosets is obtained. It is proved that lattice of all w-convex subsets of a pseudo ordered set $A$ denoted by $WCS(A)$ is lower semi modular. Also we have proved that for any two pseudo ordered sets $A$ and $A^1$, w-convex homomorphism maps atoms of $WCS(A)$ to atoms of $WCS(A^1)$. Concept of path preserving mapping is introduced in a pseudo ordered set and it is proved that every mapping of a pseudo ordered set $A$ to itself is path preserving if and only if $A$ is a cycle.

Keywords: Psoset, convex subset, w-convex subset, w-convex hull, lattice.

 Authors : N. Shilpa and S. Latha Title : On Generalized $q$-sakaguchi Type Functions Volume, Issue, Year : 7(1)(2019) Pages : 155−160

Abstract: The aim of the present paper is to study new subclasses of functions defined by using generalized sakaguchi type functions and the concept of $q$ derivative. The results investigated in this paper include coefficient inequalities, distortion inequalities, coefficient estimates etc.

Keywords: Analytic functions, $q$-calculus, Generalized Sakaguchi type function, Coefficient inequality.

 Authors : Aragaw Mulu Muhaba Title : Application of the Grey-Taguchi Method for the Optimization of Lost Wax Mold Volume, Issue, Year : 7(1)(2019) Pages : 161−169

Abstract: Investment casting technology is negligible in Ethiopia on account of the cost of investment casting is considerably higher than the sand casting due to the cost of the importation of the wax and refractory materials. In this work an attempt has been made to develop an alternative local mold material which is capable of providing hard, high strength, thermal stable shell for lost wax casting technology to manufacture intricate part. It optimizes the lost wax mold compositions based on Taguchi method and Grey relational analysis in order to obtain the particular refractory composition with optimum multiple characteristics of the mold. From Grey relational analysis response it is found optimum result that the local investment slurry with the refractory type of fired clay, its quantity of 35\%, marl clay of 4\%, water content of 23\%, wheat husk of 35\%, cow dung of 2\%, mold drying time of 24 hours and the firing temperature of 8000C. The confirmation experiments showed that the results of mold compositions were optimized for achieving the combined objectives of higher compression strength of material, lower linear and volumetric expansion value on the dried mold.

Keywords: Lost wax, Mold, Optimization, Taguchi, Grey relation.

 Authors : E. L. Mary Tency and Sr. Pauline Mary Helen Title : Vague $\widehat{g}$ Closed Set in Topological Spaces Volume, Issue, Year : 7(1)(2019) Pages : 171−176

Abstract: This paper aims to study the concepts of a new class of vague $\widehat{g}$-closed sets in vague topological space along with the basic properties of vague $\widehat{g}$-closed sets and the relationships of the set with some pre-existing sets in vague topological space.

Keywords: Vague set $(VS)$, Vague topology $(VT)$, Vague $\widehat{g}$closed set $(V\widehat{g}CS)$.

 Authors : J. Sona and N. Balamani Title : Totally $\psi$gs-Continuous Functions in Topological Spaces Volume, Issue, Year : 7(1)(2019) Pages : 177−183

Abstract: The aim of this paper is to introduce and study a new class of functions called totally $\psi$gs-continuous functions and $\psi$gs-totally continuous functions in topological spaces as a new generalization of $\psi$gs-continuity.

Keywords: Totally continuous function, $\psi$gs-continuous function, $\psi$gs-closed set and $\psi$gs-open set.

 Authors : P. Gomathi Sundari, N. Rajesh and S. Vinoth Kumar Title : Some Properties of $sg\alpha$-continuous Functions Volume, Issue, Year : 7(1)(2019) Pages : 185−193

Abstract: In \cite{rajesh:con} the authors, introduced the notion of $sg\alpha$-continuity and investigated its fundamental properties. In this paper, we investigate some more properties of this type of continuity.

Keywords: Topological spaces, $sg\alpha$-open set, $sg\alpha$-continuous function, $sg\alpha$-quotient function.

 Authors : P. Gomathi Sundari, N. Rajesh and S. Vinoth Kumar Title : Generalization of Homeomorphisms Volume, Issue, Year : 7(1)(2019) Pages : 195−202

Abstract: In this paper, we first introduce a new class of closed functions called $sg\alpha$-closed functions also introduce a new class of homeomorphisms called $sg\alpha^*$-homeomorphisms, which are weaker than homeomorphisms. We also prove that the set of all $sg\alpha^*$-homeomorphisms forms a group under the operation composition of functions.

Keywords: $sg\alpha$-open sets, $sg\alpha$-continuous functions, $sg\alpha$-irresolute functions, $sg\alpha^*$-homeomorphisms.

 Authors : P. Gomathi Sundari, R. Muthu Vijayalakshmi and N. Rajesh Title : Soft Precompactness via Soft Ideals Volume, Issue, Year : 7(1)(2019) Pages : 203−210

Abstract: In this paper, we introduce and study the concept of some covering properties via soft ideal preopen sets.

Keywords: Soft topological space, soft pre-$\tilde{I}$-compact space, soft $p$-closed space.

 Authors : P. A. Pallas Title : Hyers-Ulam Stability of the Trigintic Functional Equation in Menger Probabilistic Normed Spaces Volume, Issue, Year : 7(1)(2019) Pages : 211−219

Abstract: In this paper we examine the Hyers-Ulam stability of the trigintic functional equation in Menger probabilistic normed spaces, using the fixed point method.

Keywords: Hyers-Ulam stability, Menger Probabilistic normed spaces, trigintic functional equation, fixed point method.

 Authors : Maha A. Aldahlan Title : Type II Truncated Fr\{e}chet Generated Family of Distributions Volume, Issue, Year : 7(1)(2019) Pages : 221−228

Abstract: In this paper, we propose Type II truncated Fr\{e}chet (TIITF) generated family of distributions. Some statistical properties of the new family are derived. Type II truncated Fr\{e}chet-uniform, Type II truncated Fr\{e}chet-exponential; Type II truncated Fr\{e}chet-inverse Weibull and Type II truncated Fr\{e}chet-Rayleigh distributions are defined as sub-models. We proposed the parameters estimation of the model by using maximum likelihood (ML) method. Application of truncated Fr\{e}chet-inverse Weibull model is presented to show the importance of the suggested truncated family.

Keywords: Truncated Fr\{e}chet distribution, generated family of distributions, maximum likelihood method, Moments.

 Authors : Aragaw Mulu Muhaba Title : Optimizing Blend of Wax Pattern in the Investment Casting Process Using Grey Relational Analysis Volume, Issue, Year : 7(1)(2019) Pages : 229−238

Abstract: Nowadays investment casting is one of the most essential kinds of metal casting, it showed its effectiveness for casting materials with complicated, irregular shapes that are expensive and difficult to machine. The role of this technology is negligible in Ethiopia. This is due to the cost for importation of the wax and refractory materials. In the investment casting, poor surface finish, hardness and too much shrinkage of the wax pattern often yield poor quality of the finished casting. This paper presents optimum blend of wax for investment casting wax pattern. An optimum blend of wax could provide better surface finish, least shrinkage and enough hardness to manufacture intricate part. The test was performed generally with different types of waxes namely vegetable wax, bee wax, Paraffin wax, tree resin and Vaseline, varying their proportions and process parameter. The assessment of the influence of each blend wax on basic properties of wax pattern like surface finish, percentage shrinkage and hardness has been enriched. An attempt was made to find out the set of input parameters, which could offer a set of ideal properties of the wax blend using Grey relational Analysis. From Grey relational analysis, it is found optimum result that the local blend of wax with the vegetable wax type of Candellila, its quantity of 5\%, bee wax of 30\%, paraffin wax of 60\%, tree resin of 10\%, Vaseline of 4\%, injection temperature of $70^\circ$C and the Holding time of 2 hours. The confirmation experiments were carried out to validate the optimal results. Thus, the optimum investment mould compositions were optimized for achieving the combined objectives of higher compression strength of material, lower linear and volumetric expansion value on the dried mould considered in this work.

Keywords: Investment, Dewaxing, Wax pattern, Taguchi, Grey relation, ANOVA.

 Authors : N. Anu Title : An Overview of Fixed Point Theorems in Dislocated Quasi Metric Spaces Volume, Issue, Year : 7(1)(2019) Pages : 239−244

Abstract: This paper proposes a new results in fixed point theorems for some contraction mapping conditions in dislocated quasi metric spaces. This results generalizes several well-known results in the literature.

Keywords: Fixed point, dislocated quasi-metric spaces, dq-Cauchy, dq-converges, dq-limit, contraction mapping.

 Authors : Vivek Bansod and Mohit Sharma Title : Mathematical Approach for Twenty-Two Microtones: Frequency Ratios in Hindustani Classical Music \& their Implementation in 22 Shruti Harmonium Volume, Issue, Year : 7(1)(2019) Pages : 245−252

Abstract: This article shows the calculations of ratio's of 22 shrutis of Indian classical music relation between the Shrutis and its implementation in 22 shruti harmonium.

Keywords: Twenty-Two Microtones, Hindustani Classical Music, Shruti Harmonium.

 Authors : Gaurav Singh Sisodia Title : A Study on the Methodology of Dispersive Partial Differential Equation Volume, Issue, Year : 7(1)(2019) Pages : 253−256

Abstract: Nonlinear dispersive and wave equations are fundamental models to various regions of material science and building like plasma physical science, nonlinear optics, Bose-Einstein condensates, water waves, and general relativity. Delineations fuse the nonlinear Schrodinger, wave, Klein-Gordon, water wave, and Einstein's equations of general relativity. This field of PDE has seen an impact in development in the past twenty, most of the way by virtue of a couple of viable cross-treatments with various zones of science; mainly symphonious investigation, dynamical frameworks, and probability. It furthermore continues being a champion among the most powerful regions of investigation, rich with issues and open to various intriguing heading. The current paper highlights the methodology of dispersive partial differential equations.

Keywords: Dispersive, Equations, Differential.