Theoretical study of a -Hilfer fractional differential system in Banach spaces

This is the authors' abstract. We don't add key points for this paper.

In this work, we study the existence of solutions of nonlinear fractional coupled system of φ -Hilfer type in the frame of Banach spaces. We improve a property of a measure of noncompactness in a suitably selected Banach space. Darbo’s fixed point theorem is applied to obtain a new existence result. Finally, the validity of our result is illustrated through an example.