In this study, an effective numerical method for solving fractional differential equations using Chebyshev cardinal functions is presented. The fractional derivative is described in the Caputo sense. An operational matrix of fractional order integration is derived and is utilized to reduce the fractional differential equations to system of algebraic equations. In addition, illustrative examples...

There is a debate among contemporary mathematicians about what it really means by a fractional derivative. The question arose as a consequence of introducing a ‘new’ definition of a fractional derivative. In a reply Ortigueira and Machado [1] came up with several very important criteria to determine whether a given derivative is a fractional derivative. According to their criterion, the new fra...

This paper aims to investigate free convection heat transmission in hybrid nanofluids across an inclined pours plate, which characterizes asymmetrical nanofluid flow and transfer behavior. With angled magnetic field applied, sliding on the border of walls is also considered with sinusoidal boundary conditions. The non-dimensional leading equations are converted into a fractional model using eff...

The aim of this paper is to extend the split-step idea for the solution of fractional partial differential equations. We consider the multidimensional nonlinear Schr"{o}dinger equation with the Riesz space fractional derivative and propose an efficient numerical algorithm to obtain it's approximate solutions. To this end, we first discretize the Riesz fractional derivative then apply the Crank-...

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...

Suitable families of random variables having power series distributions are considered, and their asymptotic behavior in terms large (and moderate) deviations is studied. Two examples fractional counting processes presented, where the normalizations involved can be expressed Prabhakar function. The first example allows to consider process [Integral Transforms Spec. Funct. 27 (2016), 783–793], s...

In this article a modification of the Chebyshev collocation method is applied to the solution of space fractional differential equations.The fractional derivative is considered in the Caputo sense.The finite difference scheme and Chebyshev collocation method are used .The numerical results obtained by this way have been compared with other methods.The results show the reliability and efficiency...

‎In this article‎, we use a finite difference technique‎ ‎to solve variable-order fractional integro-differential equations‎ ‎(VOFIDEs‎, ‎for short)‎. ‎In these equations‎, ‎the variable-order fractional integration(VOFI) and‎ ‎variable-order fractional derivative (VOFD) are described in the‎ ‎Riemann-Liouville's and Caputo's sense,respectively‎. ‎Numerical experiments‎, ‎consisting of two exam...