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...

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...

*Correspondence: [email protected] Department of Mathematics and Physical Sciences, Prince Sultan University, P.O. Box 66833, Riyadh, 11586, Saudi Arabia Abstract In this article, we extend fractional calculus with nonsingular exponential kernels, initiated recently by Caputo and Fabrizio, to higher order. The extension is given to both left and right fractional derivatives and integrals. ...

This article presents the problem, in which we study unsteady double convection flow of a magnetohydrodynamics (MHD) differential-type fluid presence heat source, Newtonian heating, and Dufour effect over an infinite vertical plate with fractional mass diffusion thermal transports. The constitutive equations for flux are modeled noninteger-order derivative Caputo–Fabrizio (CF) nonsingular kerne...

A Fractional Order (FO) ProportionalIntegralDerivative (PID) controller has been proposed in this paper which works on the closed loop error and its fractional derivative and fractional integrator. FOPID is a PID controller whose derivative and integral orders are of fractional rather than integer. The extension of derivative and integral order from integer to fractional order provides more fle...

In this paper, we construct a system for analysis of an analytic solution fractional fuzzy solitary wave solutions the Korteweg–De Vries (KdV) equation. We apply iterative method and Laplace transform under Caputo-Fabrizio operator. The obtained series form was calculated approached estimate values proposed problems. upper lower portions result in all three problems were simulation applying two...

Fractional calculus is at this time an area where many models are still being developed, explored, and used in real-world applications branches of science engineering non-locality plays a key role. Although wonderful discoveries have already been reported by researchers important monographs review articles, there great deal non-local phenomena that not studied only waiting to be explored. As re...

using the riemann-liouville fractional differintegral operator, the lie theory is reformulated. the fractional poisson bracket over the fractional phase space as 3n state vector is defined to be the fractional lie derivative. its properties are outlined and proved. a theorem for the canonicity of the transformation using the exponential operator is proved. the conservation of its generator is p...