A. M. A. El-Sayed - Faculty of Sciences, Department of Mathematics, Alexandria University, Alexandria, Egypt. Sh. M. Al-Issa - Faculty of Arts and Sciences, Department of Mathematics, Lebanese International University, Saida, Lebanon. - Faculty of Arts and Sciences, Department of Mathematics, The International University of Beirut, Beirut, Lebanon. H. H. G. Hashem - Faculty of Sciences, Department of Mathematics, Alexandria University, Alexandria, Egypt. I. H. Kaddoura - Faculty of Arts and Sciences, Department of Mathematics, Lebanese International University, Saida, Lebanon. - Faculty of Arts and Sciences, Department of Mathematics, The International University of Beirut, Beirut, Lebanon. A. A. El-Bakari - Faculty of Arts and Sciences, Department of Mathematics, Lebanese International University, Saida, Lebanon.
In this paper, we investigate the existence of continuous solutions for a fractional-order hybrid non-local differential problem that involves differential feedback control. The problem is formulated with a fractional-order derivative, which adds complexity to the system’s dynamics. Our approach relies on key mathematical tools, including the Schauder fixed point theorem and the contraction mapping theorem, to establish the existence of solutions. Furthermore, we analyze the continuous dependence of the solutions on various parameters, ensuring robustness in the behavior of the system under perturbations. We present a comprehensive discussion on the solvability of the problem within the space $~L_1(I)$, providing detailed remarks on the conditions that guarantee the existence of solutions. To demonstrate the practical applicability of our results, we include an illustrative example that elucidates the theoretical results and supports the validity of our approach.
A. M. A. El-Sayed, Sh. M. Al-Issa, H. H. G. Hashem, I. H. Kaddoura, A. A. El-Bakari, Inclusive analysis of a nonlocal fractional hybrid differential problem via differential feedback control, Journal of Mathematics and Computer Science, 37 (2025), no. 4, 449--464
El-Sayed A. M. A., Al-Issa Sh. M., Hashem H. H. G., Kaddoura I. H., El-Bakari A. A., Inclusive analysis of a nonlocal fractional hybrid differential problem via differential feedback control. J Math Comput SCI-JM. (2025); 37(4):449--464
El-Sayed, A. M. A., Al-Issa, Sh. M., Hashem, H. H. G., Kaddoura, I. H., El-Bakari, A. A.. "Inclusive analysis of a nonlocal fractional hybrid differential problem via differential feedback control." Journal of Mathematics and Computer Science, 37, no. 4 (2025): 449--464
