University of Tabriz Computational Methods for Differential Equations 2345-3982 Articles in Press 2025 04 24 $\varphi$--Caputo fractional integrodifferential equations with nonlocal conditions via noncompactness measure 19705 10.22034/cmde.2025.62509.2761 EN Najat CHEFNAJ Applied Mathematics and Scientific Computing Laboratory, Sultan Moulay Slimane University, FST, Beni Mellal, Morocco. Abdellah Taqbibt Applied Mathematics and Scientific Computing Laboratory, Sultan Moulay Slimane University, FST, Beni Mellal, Morocco. Khalid Hilal Applied Mathematics and Scientific Computing Laboratory, Sultan Moulay Slimane University, FST, Beni Mellal, Morocco. M'hamed ELomari Applied Mathematics and Scientific Computing Laboratory, Sultan Moulay Slimane University, FST, Beni Mellal, Morocco. Journal Article 2024 07 15 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 concerned 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. Noncompactness measure semigroup Mönch's fixed point theorem $\varphi$-fractional derivative Integrodifferential equations https://cmde.tabrizu.ac.ir/article_19705_178b070d0bc5a70a29b214bfb5eb0ad3.pdf