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.
This work investigates the boundary value problem (BVP) of impulsive differential equations (DEs) with a nonlinear ρ−Caputo fractional and p-Laplacian operator. To prove the existence and uniqueness of solutions, we employ Schauder’s and Schaefer’s fixed point theorems, along with the Banach contraction principle. Additionally, we present two examples to show the practical applications and significance of our main results. Our study provides a new perspective on impulsive DEs with fractional and p–Laplacian operators and contributes to the development of the theory of impulsive DEs.
AMS Subject Classi cation: Primary 34A08; 34B15; secondary 34B27
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