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.
Chefnaj, N. , Taqbibt, A. , Hilal, K. and ELomari, M. (2026). $\varphi$-Caputo fractional integro-differential equations with nonlocal conditions via noncompactness measure. Computational Methods for Differential Equations, 14(3), 1458-1470. doi: 10.22034/cmde.2025.62509.2761
MLA
Chefnaj, N. , , Taqbibt, A. , , Hilal, K. , and ELomari, M. . "$\varphi$-Caputo fractional integro-differential equations with nonlocal conditions via noncompactness measure", Computational Methods for Differential Equations, 14, 3, 2026, 1458-1470. doi: 10.22034/cmde.2025.62509.2761
HARVARD
Chefnaj, N., Taqbibt, A., Hilal, K., ELomari, M. (2026). '$\varphi$-Caputo fractional integro-differential equations with nonlocal conditions via noncompactness measure', Computational Methods for Differential Equations, 14(3), pp. 1458-1470. doi: 10.22034/cmde.2025.62509.2761
CHICAGO
N. Chefnaj , A. Taqbibt , K. Hilal and M. ELomari, "$\varphi$-Caputo fractional integro-differential equations with nonlocal conditions via noncompactness measure," Computational Methods for Differential Equations, 14 3 (2026): 1458-1470, doi: 10.22034/cmde.2025.62509.2761
VANCOUVER
Chefnaj, N., Taqbibt, A., Hilal, K., ELomari, M. $\varphi$-Caputo fractional integro-differential equations with nonlocal conditions via noncompactness measure. Computational Methods for Differential Equations, 2026; 14(3): 1458-1470. doi: 10.22034/cmde.2025.62509.2761
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