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Existence of Solutions of Boundary Value Problems for Fractional Differential Equations with p-Laplacian Operator in Banach Spaces

ABSTRACT In this paper, we consider the existence of solutions for systems of nonlinear p-Laplacian fractional differential equations whose nonlinearity contains the first-order derivative explicity in Banach space E, where 𝜃 is the zero element of E, φp is the p-Laplacian operator, i.e., with p>1, its inverse function is denoted by φq with , and p,q satisfy , is standard Caputo derivative and f:I×E×E→E is continuous. Our main tool is the Sadovskii fixed point theorem.