\varphi-Caputo fractional integro-differential equations with nonlocal conditions via noncompactness measure

This article aims to prove the existence and uniqueness of solutions to fractional integro-differential equations involving the \varphi-Caputo fractional derivative with nonlocal conditions. The results are obtained using the measure of noncompactness,  probability density functions,  M\"{o}nch's fixed point theorem, and semigroup theory.   To demonstrate the applicability and effectiveness of the results, an illustrative example is presented.

کلیدواژه ها:

\phi-Caputo fractional derivative ، Semigroup theory ، Measure of noncompactness ، M‎\"{o}‎nch's fixed point theorem ، Integro-differential equations ، Nonlocal conditions