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The existence, uniqueness and the Hyers-Ulam stability of solutions for nonlinear p–Laplacian implicit Caputo-Katugampola fractional differential equations (FDEs) with multi-point generalized fractional integral boundary conditions are established. With the aid of the Leray-Schauder nonlinear alternative and the Banach contraction principle, the desired results are obtained. An example is set forth to make efficient the main results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Ulam-Hyers and the generalized Ulam-Hyers-Rassias stability results for linear fractional differential equations with hybrid proportional-Caputo derivatives in framwork of the Laplace transform method. The existence and uniqueness of solutions for nonlinear fractional differential equations with hybrid proportional-Caputo derivatives are established by means of Schaefer's fixed point theorem, Banach's fixed point theorem, and generalized Gronwall's inequality. Two examples are proposed to illustrate the main results. [ABSTRACT FROM AUTHOR]