## 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.