On Nonlinear Implicit Fractional Differential Equations with Integral Boundary Condition Involving p-Laplacian Operator without Compactness

Kamal Shah, Wajid Hussain, Phatiphat Thounthong, Piyachat Borisut, Poom Kumam, M Arif

Abstract

The motive behind this work is to obtain some sufficient conditions
for the existence of solution to a nonlinear problem of implicit fractional differential equations (IFDEs) involving integral boundary conditions with p-Laplacian
operator, using prior estimate method. The method applied here does not require
compactness of the operator, which makes it distinguished from other methods.

Besides developing the respective conditions, we also investigate Hyers-Ulam typestability for the solution of the problem under study. The validity of the established results are justified by providing a suitable example.