Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dyn...

{ Fractional calculus allows to generalize the standard (linear and one dimensional) diiusion equation by replacing the second-order space derivative by a derivative of fractional order. If this is taken as the pseudo-diierential operator introduced by Feller in 1952 the fundamental solution of the resulting diiusion equation is a probability density evolving in time and stable in the sense of ...

In this article, we prove several new fractional nabla Bennett–Leindler dynamic inequalities with the help of a simple consequence Keller’s chain rule, integration by parts, mean and Hölder’s inequality for derivative on time scales. As result this, some classical are obtained as special cases, extended our to discrete continuous calculus. addition, when α=1, shall obtain well-known instances f...

The aim of this paper is to present a new numerical method for solving the Bagley-Torvik equation. This equation has an important role in fractional calculus. The fractional derivatives are described based on the Caputo sense. Some properties of the sinc functions required for our subsequent development are given and are utilized to reduce the computation of solution of the Bagley-Torvik equati...

This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator N(ν) method, we derive the fractional solutions of the equation.

A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and other one expected utilities. In early days, Fishburn investigated SD we refer this perspective as Fishburn’s SD. his many results was development fractional-order for continuous distributions. However, discrete cannot directly generalized, because some properties fractiona...

The 1D discrete fractional Laplacian operator on a cyclically closed (periodic) linear chain with finite number N of identical particles is introduced. We suggest a ”fractional elastic harmonic potential”, and obtain the N -periodic fractional Laplacian operator in the form of a power law matrix function for the finite chain (N arbitrary not necessarily large) in explicit form. In the limiting ...

The aim of the present paper is to introduce and investigate a new subclass of Bazilevi'{c} functions in the punctured unit disk $mathcal{U}^*$ which have been described through using of the well-known fractional $q$-calculus operators, Hadamard product and a linear operator. In addition, we obtain some sufficient conditions for the func...

Fractional calculus is the generalization of integer-order calculus to rational order. This subject has at least three hundred years of history. However, it was traditionally regarded as a pure mathematical field and lacked real world applications for a very long time. In recent decades, fractional calculus has re-attracted the attention of scientists and engineers. For example, many researcher...