Issue 3 Volume 7 (2019)

Authors : Most. Ummey Kulsum and Shahanaj Pervin
Title : Exact Travelling Wave Solutions of Some Non-linear Evolution Equations Using Rational Sine-Cosine Function Method
Volume, Issue, Year : 7(3)(2019)
Pages : 1−9

Abstract: In this paper, we establish a variety of exact travelling wave solutions by using rational sine cosine function method for Boussinesq Equation, Korteweg-de Vries Equation, Gardner Equation and Generalized Boussinesq Burgers Equations which are nonlinear evolution equations. It is shown that the rational sine cosine function method provides a powerful mathematical tool for solving many nonlinear evolution equations in applied mathematics, mathematical physics and engineering.

Keywords: NLEEs, Exact Travelling Wave Solutions, Rational Sine-Cosine method.

Authors : S. B. Chandrakala, K. Manjula and B. Sooryanarayana
Title : Cordiality of Transformation Graphs of Path
Volume, Issue, Year : 7(3)(2019)
Pages : 11−21

Abstract: A graph is said to be cordial if it has a 0-1 vertex labeling that satisfies certain properties. In this paper we show that transformation graphs of path are cordial.

Keywords: Total Graph, Transformation Graph, Cordial Graphs.

Authors : S J Ghevariya
Title : Analytical Solution of Fractional BSM Differential Equation for ML-Payoff Function Using GDTM
Volume, Issue, Year : 7(3)(2019)
Pages : 23−27

Abstract: This paper contributes to the analytical solution of fractional Black-Scholes-Merton (BSM) differential equation to obtain European option pricing formula for Modified Log-payoff (ML-Payoff) function, $\max\{S\ln\big(\frac{S}{K}\big),0\}$ using Generalized Differential Transform Method (GDTM). It turns out that the BSM formula for ML-Payoff function using GDTM is quite close to the closed form solution of BSM model for ML-Payoff function.

Keywords: BSM differential equation, Fractional derivative, Generalized Differential Transform Method, ML-Payoff functions.

Authors : Ajay Dixit and Amit Ujlayan
Title : Operator Method to Solve Fractional Order Linear Differential Equations via Proportional $\alpha$ Derivative
Volume, Issue, Year : 7(3)(2019)
Pages : 29−35

Abstract: In this study, we proposed an operator method for fractional order linear differential equations with constant coefficients. The form of fractional derivative, used in this article is proportional $\alpha$ derivative, introduced recently. Furthermore, to demonstrate the efficiency of the proposed operator method for fractional differential equations some numerical examples have discussed. Finally, results are also verified for $\alpha=1$.

Keywords: Conformable fractional derivative, proportional $\alpha$ derivative, linear fractional differential equations.

Authors : S.R.Shreyas and Mayamma Joseph
Title : Characterization of Signed Double-Star Admitting Minus Dominating Function
Volume, Issue, Year : 7(3)(2019)
Pages : 37−45

Abstract: Given a signed graph $G=(V,E,\sigma)$, a function $f:V \rightarrow \{-1,0,1\}$ is a minus dominating function of $G$ if $f(u)+\sum_{v \in N(u)} \sigma(uv)f(v) \geq1$ for all $ u \hspace{0.1cm}\in V $. In this paper we characterize double star to admit an MDF and give some sufficient conditions for a general graph $G$ to admit an MDF.

Keywords: Signed graphs, Minus domination, Minus Dominating Function.

Authors : V. Revathi and P. Maheswari Naik
Title : On Quasi-class (Q) Operator
Volume, Issue, Year : 7(3)(2019)
Pages : 47−53

Abstract: In this paper we introduce the new classes of operator namely quasi-class (Q) operator acting on a complex Hilbert space H. An operator $T\in $ quasi-class (Q) if $T\left({T^{*}}^{2} T^{2} \right)=\left(T^{*} T\right)^{2} T$ where $T^{*} $ is the adjoint of the operator \textit{T}. We investigate some basic properties of this operator.

Keywords: Operator, Hilbert Space, Normal, class (Q), quasi-class (Q).

Authors : B. C. Dhage, P. R. M. Reddy, S. S. Bellale and S. D. Sarkate
Title : Dhage Iteration Method for IVPs of Nonlinear First Order Hybrid Functional Integrodifferential Equations of Neutral Type
Volume, Issue, Year : 7(3)(2019)
Pages : 55−66

Abstract: In this paper we prove an existence and approximation result for a first order initial value problems of nonlinear hybrid functional integrodifferential equations of neutral type via construction of an algorithm. The main results rely on the Dhage iteration method embodied in a recent hybrid fixed point principle of Dhage (2015) and includes the existence and approximation theorems for several functional differential equations considered earlier in the literature. An example is also furnished to illustrate the hypotheses and the abstract result of this paper.

Keywords: Hybrid neutral functional differential equation; Hybrid fixed point principle; Dhage iteration method; Existence and Approximation theorem.

Authors : Ch. Santhi Sundar Raj, B. Subrahmanyam and U. M. Swamy
Title : Fuzzy Filters of Meet-semilattices
Volume, Issue, Year : 7(3)(2019)
Pages : 67−76

Abstract: The notion of fuzzy filter of a meet-semilattice with truth values in a general frame is introduced and proved certain properties of these. In particular, it is prove that the fuzzy filters form an algebraic fuzzy system. Also, we have established a procedure to construct any fuzzy filter form a given family of filters with certain conditions. Dually, in this paper the notion of fuzzy ideal of a join-semilattice is introduced and discussed certain properties of these, which are analogues to those of fuzzy filters of meet-semilattices.

Keywords: Meet-semilattice; join-semilattice; fuzzy filter; fuzzy ideal; frame; algebraic fuzzy system.

Authors : B. Geethalakshmi and R. Hemavathy
Title : Non-self Mapping in Metric Space of Hyperbolic Type
Volume, Issue, Year : 7(3)(2019)
Pages : 77−83

Abstract: In this paper, we prove the fixed point theorem in a metric space of hyperbolic type for a pair of weakly compatible non-self mappings satisfying the generalized contraction.

Keywords: Metric space of hyperbolic type, common fixed point, non-self mapping, weakly compatible.

Authors : Andanje Mulambula, D. B. Oduor and B. Kwach
Title : Derivation of Black-Scholes-Merton Logistic Brownian Motion Differential Equation with Jump Diffusion Process
Volume, Issue, Year : 7(3)(2019)
Pages : 85−93

Abstract: Black- Scholes formed the foundation of option pricing. However, some of the assumptions like constant volatility and interest among others are practically impossible to implement hence other option pricing models have been explored to help come up with a much reliable way of predicting the price trends of options. Black-scholes assumed that the daily logarithmic returns of individual stocks are normally distributed. This is not true in practical sense especially in short term intervals because stock prices are able to reproduce the leptokurtic feature and to some extent the ``volatility smile". To address the above problem the Jump-Diffusion Model and the Kou Double-Exponential Jump-Diffusion Model were presented. But still they have not fully addressed the issue of reliable prediction because the observed implied volatility surface is skewed and tends to flatten out for longer maturities; The two models abilities to produce accurate results are reduced. This paper ventures into a research that will involve Black-Scholes-Merton logistic-type option pricing with jump diffusion. The knowledge of logistic Brownian motion will be used to develop a logistic Brownian motion with jump diffusion model for price process.

Keywords: Black-Scholes formula, Brownian motion, Logistic Brownian motion, Jump diffusion, Volatility.

Authors : Susanta Kumar Mohanta
Title : On Eta-Directional Derivative
Volume, Issue, Year : 7(3)(2019)
Pages : 95−102

Abstract: The primary objective of this article is to introduced generalized directional derivative($\eta$-directional derivative) of a function in the direction of a certain function in Linear spaces, Hilbert spaces and Banach spaces. This will be the generalization of Frechet derivative, Gauteaux derivative and Hadamard derivative under certain conditions. Some properties of $\eta$-directional derivative with there examples have been studied.

Keywords: Frechet derivative, Gauteaux derivative, Hadamard derivative, $\eta$-invex set, Normalized vector function.

Authors : Sarfraz Ahmed and Tapan Boruah
Title : Application of Soft Matrix Theory in Decision Making
Volume, Issue, Year : 7(3)(2019)
Pages : 103−109

Abstract: In this paper, the traditional soft set theory is expanded to be a fuzzy one the fuzzy membership is used to describe parameter-approximate elements of fuzzy soft set. We then define products of soft matrices and their properties. We finally construct a soft max-min decision making method which can be successfully applied to the problem that contains uncertainties.

Keywords: Soft sets Soft matrix, Products of soft matrices, Soft max-min decision making.

Authors : Litegebe Wondie and Satish Kumar
Title : Bounds of Mean Code Word Lenth With Generalized Information Measure and its Application in Coding Theory
Volume, Issue, Year : 7(3)(2019)
Pages : 111−117

Abstract: In this communication, we find a lower and upper bounds for mean code word length for complete and incomplete probability distribution with generalized information measure and we identify its application in coding theory.

Keywords: Shannon inequality, Tsalli's entropy, Codeword length, Kraft inequality.

Authors : S. J. Ghevariya
Title : Solution of BSM Differential Equation with Time Dependent Parameters for Standard Powered Option
Volume, Issue, Year : 7(3)(2019)
Pages : 119−121

Abstract: This paper deals to the solution of Black-Scholes-Merton (BSM) differential equation with time dependent parameters for standard powered option which is a generalization of well known plain vanilla option.

Keywords: BSM differential equation; BSM model; plain vanilla option, standard powered option.

Authors : T. Srinivasarao and G. Ashok
Title : Not Distributive Lattice Over Residue Classes Polynomial Ring
Volume, Issue, Year : 7(3)(2019)
Pages : 123−125

Abstract: In the era of soft skills and almost every area of physical activity and space, the shied ankle role player is data security. However safe the data may be today by creating the firewall, in few hours or days, those firewalls are pierced through and the data will be hacked/stolen. So, every moment, there is a need for creating new firewalls or new techniques in security systems. Ciphering through algebraic techniques is my view point and taking a lattice based on algebra and failure of distributive property may be considered as a productive approach that enciphers a code and deciphering may be difficult while there is no regularity/balance in the system. The polynomial ring defined over a finite field of residue classes modulo \textit{p } where \textit{p} is a prime, is a commutative ring with unity. A principal ideal generated by an irreducible polynomial is a maximal ideal in that ring. So, the theorem `if \textit{R} is a commutative ring with unity, \textit{M} is an ideal of \textit{R}, then \textit{M} is maximal if and only if the quotient ring of \textit{R} by \textit{M} is a field'', helps us to construct a field. Defining the `join' denoted by `$\vee $' and `meet' , `$\wedge $' operations on this field using the modulo \textit{p} operation both on the coefficient and exponent of each monomial of each polynomial will allow the closedness under these operations and thus the formed lattice is a closed algebra. In the present discussion, we restrict our view to the elements of $\mathbb{Z}_{5}^{5} \left[x\right]$ up to distributive property.

Keywords: Residue classes, polynomial ring, field, join; meet, integration modulo 5, differentiation modulo 5, supremum and infimum, Congruent and Equivalent polynomials, Distributive laws.

Authors : G. R. Roshini, S. B. Chandrakala, R. Indira and B. Sooryanarayana
Title : Non-Neighbor Reduced Randic and Sum-Connectivity Index
Volume, Issue, Year : 7(3)(2019)
Pages : 127−133

Abstract: In this article, we have computed the non-neighbor reduced-Randic, sum-connectivity index and multiplicative non-neighbor reduced-Randic, sum-connectivity index for some standard graphs and for corona product of some graphs.

Keywords: Topological index, non-neighbors vertices, reduced topological indices.

Authors : S. S. Phulsagar
Title : Dynamical Analysis of Michaelis-Menten Enzyme Reactions
Volume, Issue, Year : 7(3)(2019)
Pages : 135−141

Abstract: In this paper Michaelis-Menten type enzyme reactions are studied. With an output of this kind one could consider the following set of equations $\frac{dx}{d\tau }=a-bx-x^py^q$, $\frac{dy}{d\tau }=x^py^q-\frac{cy}{y+1} $. Taking some particular values of the parameters \textit{a, b, p, q } a detailed analysis of the system is taken up. The system is analysed by studying the associated differential equations, phase plane analysis and bifurcation analysis.

Keywords: Enzyme reactions, Michaelis-Menten, system of differential equations, equilibrium points, phase plane, bifurcation analysis.