Stability of a fractional heat equation with memory

Authors

  • S. Kerbal Sultan Qaboos Univeristy, PO Box 36, Al-Khoud 123, Muscat, Oman https://orcid.org/0000-0001-5728-0419
  • N. Tatar King Fahd University of Petroleum and Minerals, Dhahran 31261, Dhahran, Saudi Arabia
https://doi.org/10.15330/cmp.16.1.328-345

Keywords:

Caputo fractional derivative, heat-conduction, memory term, Mittag-Leffler stability, multiplier technique
Published online: 2024-06-30

Abstract

Of concern is a fractional differential problem of order between zero and one. The model generalizes an existing well-known problem in heat conduction theory with memory. First, we justify the replacement of the first order derivative by a fractional one. Then, we establish a Mittag-Leffler stability result for a class of heat flux relaxation functions. We will combine the energy method with some properties from fractional calculus.

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How to Cite
(1)
Kerbal, S.; Tatar, N. Stability of a Fractional Heat Equation With Memory. Carpathian Math. Publ. 2024, 16, 328-345.