Nonlinear generalized fractional differential equations with generalized fractional integral conditions

By Samiha Belmor, Chokkalingam Ravichandran, Fahd Jarad. Journal of Taibah University for Science, 2020

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This research work is dedicated to an investigation of the existence and uniqueness of a class of nonlinear ψ-Caputo fractional differential equation on a finite interval $[0, T] $[0,T], equipped with nonlinear ψ-Riemann–Liouville fractional integral boundary conditions of different orders $0 \lt \alpha , \beta \lt 1 $0<α,β<1, we deal with a recently introduced ψ-Caputo fractional derivative of order $1 \lt q\leq ~2 $1<q≤2. The formulated problem will be transformed into an integral equation with the help of Green function. A full analysis of existence and uniqueness of solutions is proved using fixed point theorems: Leray–Schauder nonlinear alternative, Krasnoselskii and Schauder's fixed point theorems, Banach's and Boyd–Wong's contraction principles. We show that this class generalizes several other existing classes of fractional-order differential equations, and therefore the freedom of choice of the standard fractional operator. As an application, we provide an example to demonstrate the validity of our results.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

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