Existence and numerical solutions of a coupled system of integral BVP for fractional differential equations

Abstract

This paper is devoted to establishing the existence theory for at least one solution to a coupled system of fractional order differential equations (FDEs). The problem under consideration is subjected to movable type integral boundary conditions over a finite time interval. Furthermore, we investigate the approximate solutions to the considered problem with the help of the differential transform. Moreover, some necessary conditions for the Hyers-Ulam type stability to the solution of the proposed problem are developed. The whole investigation has been illustrated by providing some suitable examples.

Two‐weight norm inequalities for fractional maximal functions and fractional integral operators on weighted Morrey spaces

“…Fractional type operators are a class of important operators in harmonic analysis and were widely used in the study of partial differential equations and function spaces [1, 2, 4–6, 9, 15, 20, 22, 30]. Recall that the fractional maximal function and the fractional integral operator are defined by and respectively, where f is a locally integrable function defined on and Q takes over all cubes in which contain x .…”

Solvability for some class of multi-order nonlinear fractional systems

“…Furthermore, the study of fractional systems has also been a topic focused on; see [19][20][21][22][23][24][25]. Although the coupled systems of fractional boundary value problems have been considered by some authors, coupled systems with multi-order fractional orders are seldom discussed.…”

“…Although the coupled systems of fractional boundary value problems have been considered by some authors, coupled systems with multi-order fractional orders are seldom discussed. The orders of the nonlinear fractional systems which are considered in the existing papers belong to the same interval (n, n + 1] (n ∈ N + ); see [19][20][21][22][23][24].…”

Numerical Solution of Fractional Boundary Value Problems by Using Chebyshev Wavelet Method

“…In the present research work, the CWM is fully compatible with the complexity of the problems and has shown extremely accurate results, especially in case of fractional linear and nonlinear boundary problems of fourth, sixth and eighth order [21][22][23][24][25][26][27]. Some other well -known methods for the solution of fractional differential equations are given in [28][29][30][31][32][33].…”