Existence of solutions for fractional integral boundary value problems with p(t) -Laplacian operator

Abstract

This paper aims to investigate the existence of solutions for fractional integral boundary value problems (BVPs for short) with p(t)-Laplacian operator. By using the fixed point theorem and the coincidence degree theory, two existence results are obtained, which enrich existing literatures. Some examples are supplied to verify our main results.

Existence of solutions for weighted p(t)-Laplacian mixed Caputo fractional differential equations at resonance

“…Moreover, considerable attention is paid to p-Laplacian differential equations due to their importance in theory and application of mathematics and physics. Recently, the existence, uniqueness and the stability of solutions for differential equations with p(t)-Laplacian operator is studied in some papers [30][31][32], which is an interesting subject for investigation.…”

“…In [30], the authors investigated the existence and uniqueness of solution by the use of some fixed point theorems and Mawhin's coincidence degree, in resonance and non resonance cases, for the following Riemann-Liouville fractional boundary value problem:…”

Existence of solutions for Erdélyi–Kober fractional integral boundary value problems with $p ( t )$-Laplacian operator

“…are continuous. After that, Shen and Liu [24] studied the following integral boundary value problem of fractional differential equations with p(t)-Laplacian operator at non-resonance or resonance:…”