Existence of solution for a tripled system of fractional hybrid differential equations with laplacie involving Caputo derivatives

In this paper, we study the existence of solutions for a tripled system of Fractional hybrid differential equations with nonlocal integro multi point boundary conditions by using the Laplacian operator of degree p and the Caputo derivatives, we know that the differential equations with the Laplacian operator appeared for the first time when Leibenson was attempting to derive an accurate formula to model turbulent flow in the porous medium, in this work we study the case of the Fractional hybrid differential equations who are the quadratic perturbations of nonlinear differential equations. Dhage and Lakshmikantham [12] discussed the hybrid differential equation They established the existence, uniqueness results, and some fundamental differential inequalities for hybrid differential equations initiating the study of the theory of such systems and proved to utilize the theory of inequalities, its existence of extremal solutions, and comparison results. Hilal and Kajouni [19] have studied boundary fractional hybrid differential equations involving Caputo differential operators, so In this article, we are interested in the existence result of the solution of hybrid nonlinear differential equations. obtained by the hybrid fixed point theorem for a sum of three operators due to Dhage. An illustrative example is presented at the end to show the applicability of the results. To the best of our knowledge, this is the first time where such problem is considered.