"Well-Posedness of General Time-Fractional Diffusion Equations Involvin" by Soraya Abdelaziz, Nabil Shawagfeh et al.

Progress in Fractional Differentiation & Applications

Article Title

Well-Posedness of General Time-Fractional Diffusion Equations Involving Atangana-Baleanu Derivative

Authors

Soraya Abdelaziz, Department of Mathematics, The University of Jordan, Amman 11942, JordanFollow
Nabil Shawagfeh, Department of Mathematics, The University of Jordan, Amman 11942, JordanFollow
Mohammed Al-Refai, Department of Mathematics,Yarmouk University, Irbid, JordanFollow

Author Country (or Countries)

Jordan

Abstract

In this paper, we study a general time-fractional diffusion equation involving the Atangana-Baleanu derivative of Caputo sense. First, we derive weak maximum-minimum principles to the associated fractional differential operators of the parabolic type, then we apply these principles to establish uniqueness and stability results to initial-boundary value problem and to obtain a norm estimate of the solution. For the existence of solution to the problem, we apply the eigenfunction expansion method to construct a formal solution, which under certain conditions proved to be a weak solution.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/090108

Recommended Citation

Abdelaziz, Soraya; Shawagfeh, Nabil; and Al-Refai, Mohammed (2023) "Well-Posedness of General Time-Fractional Diffusion Equations Involving Atangana-Baleanu Derivative," Progress in Fractional Differentiation & Applications: Vol. 9: Iss. 1, Article 8.
DOI: http://dx.doi.org/10.18576/pfda/090108
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol9/iss1/8

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