Extremal Solutions and Relaxation Problems for Fractional Differential Inclusions

Abstract

We present the existence of extremal solution and relaxation problem for fractional differential inclusion with initial conditions.

Existence of Solutions for a Class of Caputo Fractional q-Difference Inclusion on Multifunctions by Computational Results

“…Denote by AC[0, 1] the space of all the absolutely continuous functions defined on J. By using main idea of [15,16,41], we define the set of selections of F by…”

An increasing variables singular system of fractional q-differential equations via numerical calculations

“…is a Banach space [43]. Similar to the idea of the works [44,45], define the set of the selections of S at k by S = k = (k 1 , k 2 , . .…”

The existence of solution for a k-dimensional system of fractional differential inclusions with anti-periodic boundary value conditions

“…) is a Banach space ( [31]). By using the idea of the papers [4], [6], [27] and [32], we define the set of the selections of F i at x by…”

“…There are many published many works about the existence of solutions for many fractional differential equations by using fixed point theory (see for example, [8]- [12], [25]- [28] and the references there in). Also, some researchers tried to obtain solutions of fractional differential inclusions by using different conditions (see for example, [1]- [7], [14]- [17], [20], [25], [27]- [28], [32] and the references there in). One can find more details elementary notions on fractional differential equations in [22], [26] and [30].…”