Existence of positive solutions for p-Laplacian boundary value problems of fractional differential equations

Abstract

Abstract In this paper, we study the existence and multiplicity of ρ-concave positive solutions for a p-Laplacian boundary value problem of two-sided fractional differential equations involving generalized-Caputo fractional derivatives. Using Guo–Krasnoselskii fixed point theorem and under some additional assumptions, we prove some important results and obtain the existence of at least three solutions. To establish the results, Green functions are used to transform the considered two-sided generalized Katugampola and Caputo fractional derivatives. Finally, applications with illustrative examples are presented to show the validity and correctness of the obtained results.

Keywords

• Fractional differential equations
• p-Laplacian
• Generalized Caputo fractional derivative
• Concave
• Positive solutions