Articles in PressVolume 7, Issue 3 (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.