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In this research paper, we dedicate our interest to an investigation of the sufficient conditions for the existence of solutions of two new types of a coupled systems of hybrid fractional differential equations involving ϕ-Hilfer fractional derivatives. The existence results are established in the weighted space of functions using Dhage’s hybrid fixed point theorem for three operators in a Banach algebra and Dhage’s helpful generalization of Krasnoselskii fixed- point theorem. Finally, simulated examples are provided to demonstrate the obtained results.

In this work, we present the existence, uniqueness, and stability result of solution to the nonlinear fractional dierential equations involving HilferKatugampola derivative subject to nonlocal fractional integral boundary conditions. The reasoning is mainly based upon properties of Mittag-Leer functions, and xed-point methods such as Banach contraction principle and Krasnoselskii's xed point theorem. Moreover, the generalized Gornwall inequality lemma is used to analyze dierent types of stability. Finally, one example is given to illustrate our theoretical results.