Solvability for the ψ-Caputo-Type Fractional Differential System with the Generalized p-Laplacian Operator

Abstract

In this article, by combining a recent critical point theorem and several theories of the ψ-Caputo fractional operator, the multiplicity results of at least three distinct weak solutions are obtained for a new ψ-Caputo-type fractional differential system including the generalized p-Laplacian operator. It is noted that the nonlinear functions do not need to adapt certain asymptotic conditions in the paper, but, instead, are replaced by some simple algebraic conditions. Moreover, an evaluation criterion of the equation without solutions is also provided. Finally, two examples are given to demonstrate that the ψ-Caputo fractional operator is more accurate and can adapt to deal with complex system modeling problems by changing different weight functions.