K. O. Melha - Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, 02180, Ouled Fares, Chlef, Algeria. S. T. M. Thabet - Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, 602105, Tamilnadu, India. - Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen. - Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02814, Republic of Korea. A. M. Djaouti - Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Hofuf 31982, Al-Ahsa, Saudi Arabia. I. Kedim - Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia. K. Aldwoah - Department of Mathematics, Faculty of Science, Department of Mathematics, Faculty of Science, 42351 Madinah, Saudi Arabia. M. Vivas-Cortez - Faculty of Exact, Natural and Environmental Sciences, Pontificia Universidad Catolica del Ecuador, FRACTAL (Fractional Research in Analysis, Convexity and Their Applications Laboratory), Av. 12 de octubre 1076 y Roca, Apartado Quito 17-01-2184, Ecuador.
This article studies a sequential time-fractional diffusion equation characterized by the Caputo derivative. We establish the existence of a mild solution using the resolvent operator and Schaefer's fixed point technique. Moreover, we explore Ulam-Hyers and Ulam-Hyers-Rassias stabilities through nonlinear methods. The study also presents examples of applications of these techniques, such as application to a partial Caputo time-fractional diffusion equation.
K. O. Melha, S. T. M. Thabet, A. M. Djaouti, I. Kedim, K. Aldwoah, M. Vivas-Cortez, Existence and stability of a mild solution to an abstract sequential time-fractional diffusion equation of pantograph type, Journal of Mathematics and Computer Science, 41 (2026), no. 3, 421--436
Melha K. O., Thabet S. T. M., Djaouti A. M., Kedim I., Aldwoah K., Vivas-Cortez M., Existence and stability of a mild solution to an abstract sequential time-fractional diffusion equation of pantograph type. J Math Comput SCI-JM. (2026); 41(3):421--436
Melha, K. O., Thabet, S. T. M., Djaouti, A. M., Kedim, I., Aldwoah, K., Vivas-Cortez, M.. "Existence and stability of a mild solution to an abstract sequential time-fractional diffusion equation of pantograph type." Journal of Mathematics and Computer Science, 41, no. 3 (2026): 421--436
