Solvability of Caputo-Katugampola Fractional Differential Equation Involving <i>p</i>-Laplacian at Resonance

In this paper, we investigate the existence of solutions for Caputo-Katugampola fractional differential equations at resonance that involve two different orders and the p-Laplacian operator, by using the theory of the coincidence degree due to Mawhin and improving it due to Ge’s theory. The dimension of the kernel for a fractional differential operator is two or one according to the value of type of Katugampola fractional integral. We use inequalities and nonlinear analytic techniques to investigate the existence of the solutions. In the simplest case, we automatically found the solvability of the Caputo-Katugampola equations with p-Laplacian operator. We provide two examples to illustrate our results.