TY - JOUR
T1 - Existence and stability of a mild solution to an abstract sequential time-fractional diffusion equation of pantograph type
AU - Melha, Khellaf Ould
AU - Thabet, Sabri T.M.
AU - Djaouti, Abdelhamid Mohammed
AU - Kedim, Imed
AU - Aldwoah, Khaled
AU - Vivas-Cortez, Miguel
N1 - Publisher Copyright:
©2026 All rights reserved.
PY - 2026
Y1 - 2026
N2 - 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.
AB - 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.
KW - Caputo fractional derivative (CFD)
KW - pantograph problem
KW - resolvent operator (R-operator)
KW - time-fractional diffusion equation (TFDE)
KW - Ulam-Hyers-Rassias stability (UHR-S)
UR - https://www.scopus.com/pages/publications/105022253082
U2 - 10.22436/jmcs.041.03.08
DO - 10.22436/jmcs.041.03.08
M3 - Article
AN - SCOPUS:105022253082
SN - 2008-949X
VL - 41
SP - 421
EP - 436
JO - Journal of Mathematics and Computer Science
JF - Journal of Mathematics and Computer Science
IS - 3
ER -