The objective of this work is to investigate the existence and uniqueness of the solution to a nonlinear fractional integro-differential equation with a non-local condition involving the generalized fractional proportional Caputo derivative of two distinct orders. To achieve this, Krasnoselskii’s fixed point theorem is utilized to examine the existence of the solution, followed by the application of Banach’s fixed point theorem to study the uniqueness. Lastly, two illustrative examples are provided to highlight the main results.
Zerbib, S. , Hilal, K. and Kajouni, A. (2025). Nonlocal Caputo generalized proportional fractional integro-differential systems: an existence study. Journal of Mathematical Modeling, 13(2), 375-391. doi: 10.22124/jmm.2024.29126.2594
MLA
Zerbib, S. , , Hilal, K. , and Kajouni, A. . "Nonlocal Caputo generalized proportional fractional integro-differential systems: an existence study", Journal of Mathematical Modeling, 13, 2, 2025, 375-391. doi: 10.22124/jmm.2024.29126.2594
HARVARD
Zerbib, S., Hilal, K., Kajouni, A. (2025). 'Nonlocal Caputo generalized proportional fractional integro-differential systems: an existence study', Journal of Mathematical Modeling, 13(2), pp. 375-391. doi: 10.22124/jmm.2024.29126.2594
CHICAGO
S. Zerbib , K. Hilal and A. Kajouni, "Nonlocal Caputo generalized proportional fractional integro-differential systems: an existence study," Journal of Mathematical Modeling, 13 2 (2025): 375-391, doi: 10.22124/jmm.2024.29126.2594
VANCOUVER
Zerbib, S., Hilal, K., Kajouni, A. Nonlocal Caputo generalized proportional fractional integro-differential systems: an existence study. Journal of Mathematical Modeling, 2025; 13(2): 375-391. doi: 10.22124/jmm.2024.29126.2594
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