Nonlocal boundary value problems for fractional differential inclusions with Erdélyi-Kober fractional integral boundary conditions

Abstract

ABSTRACT:We study a new class of boundary value problems consisting of a fractional differential inclusion of Riemann-Liouville type and Erdélyi-Kober fractional integral conditions. Some new existence results for convex as well as nonconvex multivalued maps are obtained by using standard fixed-point theorems. Some illustrative examples are also presented.

On a New Modification of the Erdélyi–Kober Fractional Derivative

“…with ρ > 0 and η ∈ I R. The E-K fractional integral operator has been used to solve single, double and triple integral equations that have spatial functions of mathematical physics in their kernels. Some applications and properties of the E-K fractional integral operator can be found in [1,5,[8][9][10][11][12][13][14][15][16][17][18] and references therein. Based on the fractional integral operator given in Equation (6), the E-K fractional derivative operator, D α a+;ρ,η , of order α > 0, where n − 1 < α ≤ n, ρ > 0 and η ∈ I R, is defined as: [1,5] D α a+;ρ,η f (t) = t −ρη 1 ρt ρ−1 d dt n t ρ(n+η) I n−α a+;ρ,η+α f (t), t > a ≥ 0.…”