W. Sudsutad - Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand. C. Thaiprayoon - Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand. J. Kongson - Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand. A. Aphithana - Division of Mathematics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Krungthep, Bangkok 10120, Thailand.
This work obtained a novel nonlinear coupled Ambartsumian system subject to nonlocal integral conditions with the \((k,\psi)\)-Hilfer proportional fractional operator. According to this study, we presented an extended \((k,\psi)\)-Hilfer proportional fractional Gronwall inequality. The results concerning existence and uniqueness were established by employing the fixed point theory of Banach's and Krasnosel'skii's types. Furthermore, a variety of stability in the context of Ulam-Hyers-Mittag-Leffler and Ulam-Hyers-Rassias-Mittag-Leffler were investigated. In addition, two numerical examples were demonstrated to illustrate and apply the main results by using a novel numerical technique based on decomposition formula.
W. Sudsutad, C. Thaiprayoon, J. Kongson, A. Aphithana, Application of an extended Gronwall-type inequality for a \((k,\psi)\)-Hilfer proportional fractional Ambartsumian system via nonlocal integral conditions, Journal of Mathematics and Computer Science, 41 (2026), no. 4, 456--486
Sudsutad W., Thaiprayoon C., Kongson J., Aphithana A., Application of an extended Gronwall-type inequality for a \((k,\psi)\)-Hilfer proportional fractional Ambartsumian system via nonlocal integral conditions. J Math Comput SCI-JM. (2026); 41(4):456--486
Sudsutad, W., Thaiprayoon, C., Kongson, J., Aphithana, A.. "Application of an extended Gronwall-type inequality for a \((k,\psi)\)-Hilfer proportional fractional Ambartsumian system via nonlocal integral conditions." Journal of Mathematics and Computer Science, 41, no. 4 (2026): 456--486
