Showing papers in "Mathematical Methods in The Applied Sciences in 2019"

Stability of the fractional Volterra integro‐differential equation by means of ψ‐Hilfer operator

Abstract: In this paper, using the Riemann-Liouville fractional integral with respect to another function and the $\\psi-$Hilfer fractional derivative, we propose a fractional Volterra integral equation and the fractional Volterra integro-differential equation. In this sense, for this new fractional Volterra integro-differential equation, we study the Ulam-Hyers stability and, also, the fractional Volterra integral equation in the Banach space, by means of the Banach fixed-point theorem. As an application, we present the Ulam-Hyers stability using the $\\alpha$-resolvent operator in the Sobolev space $W^{1,1}(\\mathbb{R}_{+},\\mathbb{C})$.

Ulam‐Hyers stability of Caputo fractional difference equations

Abstract: Funding information Sun Yat-sen University; The International Program for Ph.D. Candidates We study the Ulam-Hyers stability of linear and nonlinear nabla fractional Caputo difference equations on finite intervals. Our main tool used is a recently established generalized Gronwall inequality, which allows us to give some Ulam-Hyers stability results of discrete fractional Caputo equations. We present two examples to illustrate our main results.

Delayed perturbation of Mittag‐Leffler functions and their applications to fractional linear delay differential equations

Abstract: In this paper, we propose a delayed perturbation of Mittag-Leffler type matrix function, which is an extension of the classical Mittag-Leffler type matrix function and delayed Mittag-Leffler type matrix function. With the help of the delayed perturbation of Mittag-Leffler type matrix function, we give an explicit formula of solutions to linear nonhomogeneous fractional delay differential equations.