New class of boundary value problem for nonlinear fractional differential equations involving Erdélyi-Kober derivative

Arioua, Yacine   ; Titraoui, Maria

Communications in Mathematics, Tome 27 (2019) no. 2, pp. 113-141

Abstract (VO)

In this paper, we introduce a new class of boundary value problem for nonlinear fractional differential equations involving the Erdélyi-Kober differential operator on an infinite interval. Existence and uniqueness results for a positive solution of the given problem are obtained by using the Banach contraction principle, the Leray-Schauder nonlinear alternative, and Guo-Krasnosel'skii fixed point theorem in a special Banach space. To that end, some examples are presented to illustrate the usefulness of our main results.

Détail

Classification : 34A08, 34A37, 47H10
Keywords: Fractional differential equations; Boundary value problems; Erdélyi-Kober derivative; Fixed point theorems; Existence; Uniqueness.

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