Nonlinear Riemann-Liouville Fractional Differential Equations With Nonlocal Erdélyi-Kober Fractional Integral Conditions

Abstract

In this paper we study a new class of Riemann-Liouville fractional differential equations subject to nonlocal Erdélyi-Kober fractional integral boundary conditions. Existence and uniqueness results are obtained by using a variety of fixed point theorems, such as Banach fixed point theorem, Nonlinear Contractions, Krasnoselskii fixed point theorem, Leray-Schauder Nonlinear Alternative and Leray-Schauder degree theory. Examples illustrating the obtained results are also presented.

Katugampola Fractional Differential Equation with Erdelyi-Kober Integral Boundary Conditions

“…Classical fractional order boundary conditions involve Riemman-Liouville or Katugampola type integral boundary conditions, which use Erdelyi-Kober fractional integral operators. Introduced by Arther Erdelyi and Herman Kober in 1940 [19], they play an important role in solving some problems in signal processing, dual and triple integral equations, and special function in mathematical physics [1,7,9,11,5,18,21].…”

“…In [19], the authors established the existence of solution for following nonlinear Riemann-Liouville fractional dierential equation subject to nonlocal Erdelyi-Kober fractional integral conditions:…”

On a Hilfer fractional differential equation with nonlocal Erdélyi-Kober fractional integral boundary conditions

“…In the past few years, the Erdélyi-Kober fractional derivative, as a generalization of the Riemann-Liouville fractional derivative, is often used, too [28,31]. An Erdélyi-Kober operator is a fractional integration operation introduced by Arthur Erdélyi and Hermann Kober in 1940 [19].…”

A Study of Nonlinear Fractional-Order Boundary Value Problem With Nonlocal Erdelyi-Kober and Generalized Riemann-Liouville Type Integral Boundary Conditions

“…Fractional differential equations supplemented with a variety of initial and boundary conditions have been investigated by several researchers and the literature on the topic is now much enriched. For examples and recent development of the topic, see [1,3,4,5,6,7,9,12,13,21,22,24,25,30,31,32] and the references cited therein.…”