It has a wide application in the problem of physics, chemistry, biology, engineering and applied sciences. The theory Bessel functions is intimately connected with certain types differential equations. A detail account applications are given book Watson [26]. In this present paper, we establish generalized extension k-Bessel-Maitland function involving pathway integral operator. obtain composit...

We introduce a bivariate distribution supported on the first quadrant with exponential, and heavy tailed Mittag–Leffer, marginal distributions. Although this distribution belongs to the class of geometric operator stable laws, it is a rather special case that does not follow their general theory. Our results include the joint density and distribution function, Laplace transform, conditional dis...

in this paper, we consider the inhomogeneous time-fractional nonlinear fisher equation with three known boundary conditions. we first apply a modified homotopy perturbation method for translating the proposed problem to a set of linear problems. then we use the separation variables  method to solve obtained problems. in examples, we illustrate that by right choice of source term in the modified...

The purpose of this paper is to investigate some qualitative properties solutions nonlinear fractional retarded Volterra integro-differential equations (FrRIDEs) with Caputo derivatives. These include uniform stability, asymptotic Mittag–Leffer stability and boundedness. presented results are proved by defining an appropriate Lyapunov function applying the Lyapunov–Razumikhin method (LRM). Henc...

in this paper, we consider the inhomogeneous time-fractional nonlinear fisher equation with three known boundary conditions. we first apply a modified homotopy perturbation method for translating the proposed problem to a set of linear problems. then we use the separation variables  method to solve obtained problems. in examples, we illustrate that by right choice of source term in the modified...

Abstract We develop a first-principles approach to define the communicability between two nodes in time-varying network with memory. The formulation is based on time-fractional Schrödinger equation, where fractional (of Caputo type) derivative accounts for memory of system. Using Hamiltonian tight-binding formalism we propose temporal as product Mittag-Leffer functions adjacency matrices snapsh...

The aim of this work is to elaborate and define the idea refined convex function Raina type. In addition, we have attained some associated properties in manner newly introduced idea. To add more comprehension into investigated definition, obtain estimations Hermite-Hadamard inequality. For reader’s interest, remarks regarding Mittag-Leffer function. During last four decades, term Mitag-Leffler ...

this article is devoted to study of the autoconvolution equations and generalized mittag-leffler functions. these types of equations are given in terms of the laplace transform convolution of a function with itself. we state new classes of the autoconvolution equations of the first kind and show that the generalized mittag-leffler functions are solutions of these types of equations. in view of ...