On Implicit Coupled Hadamard Fractional Differential Equations with Generalized Hadamard Fractional Integro-Differential Boundary Conditions

This study is devoted to studying the existence and uniqueness of solutions for Hadamard implicit fractional differential equations with generalized Hadamard fractional integro-differential boundary conditions by utilizing the contraction principle of the Banach and Leray-Schauder fixed point theorems. Moreover, with two different approaches, the Hyers-Ulam stabilities are also discussed. Different ordinary differential equations of the third order with different boundary conditions (e.g., initial, anti periodic and integro-differential) can be obtained as a special case for our proposed model. Finally, for verification, an example is presented, and some graphs for the particular variables and particular functions are drawn using MATLAB.