O. Zentar - Department of Computer Science, University of Tiaret, Tiaret, Algeria. - Laboratory of Research in Artificial Intelligence and Systems (LRAIS), University of Tiaret, Algeria. M. Ziane - Department of Mathematics, University of Tiaret, Tiaret, Algeria. - Laboratory of Research in Artificial Intelligence and Systems (LRAIS), University of Tiaret, Algeria. A. G. Alshanti - Department of Mathematics, Al-Zaytoonah University of Jordan, Amman 11733, Jordan. M. A. Hammad - Department of Mathematics, Al-Zaytoonah University of Jordan, Amman 11733, Jordan.
This paper focuses on a class of nonlinear switched fractional systems governed by the tempered \((k,\varphi)\)-Hilfer derivative. First, we generalize a Gronwall-type inequality involving the tempered \((k,\varphi)\)-integral operator. Second, the nonlinear alternative for condensing maps and the Banach contraction theorem are used to establish new quantitative results. Third, a stability in the Ulam sense is explored. Finally, we illustrate our findings with examples.
O. Zentar, M. Ziane, A. G. Alshanti, M. A. Hammad, On the implicit switched coupled fractional system of tempered \((k,\varphi)\)-Hilfer type, Journal of Mathematics and Computer Science, 40 (2026), no. 2, 135--155
Zentar O., Ziane M., Alshanti A. G., Hammad M. A., On the implicit switched coupled fractional system of tempered \((k,\varphi)\)-Hilfer type. J Math Comput SCI-JM. (2026); 40(2):135--155
Zentar, O., Ziane, M., Alshanti, A. G., Hammad, M. A.. "On the implicit switched coupled fractional system of tempered \((k,\varphi)\)-Hilfer type." Journal of Mathematics and Computer Science, 40, no. 2 (2026): 135--155
