Date:
Speaker: Fatma Al-Musalhi, Sultan Qaboos University, Oman
Time : 15:00 - 16.00 CEST (Rome/Paris)
Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy
Zoom : A zoom meeitng link will appear here, one hour before the talk
Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)
* SISSA, International School of Advanced Studies, Italy
** Eastern Mediterranean University, Northern Cyprus
Keywords: Fractional differential equations, Explicit solutions, Transmutation relations
Abstract: Fractional differential equations (FDEs) are widely used to describe complex processes such as diffusion, material behavior, and control systems.
In this talk, we study two methods for solving FDEs with continuous variable coefficients. The first method employs the fixed point theorem. We consider multi-term fractional differential equations with continuous variable coefficients and Erd´elyi-Kober-type differential operators with multiple independent fractional orders [2]. We solve such equations within a general framework, obtaining explicit solutions in the form of uniformly convergent series. By examining several particular cases, we verify the consistency of our results with those previously obtained in the literature [1, 3, 4].
The second method, which builds on the first, is based on the transmutation relations approach. Since classical FDEs can be solved using fixed point theory, we use transmutation relation to extend these results to broader classes of fractional operators. We express the fractional derivative in transmuted form and then transform the FDEs involving these transmuted operators into forms involving more classical fractional derivatives, which have been extensively analyzed and solved in the literature. We consider specific types of fractional operators, including weighted fractional derivatives with respect to a function, tempered derivatives, and Hadamard-type fractional derivatives. These equations are reduced to ones involving the Caputo fractional derivative, whose solutions are already known and can be expressed explicitly in series form in terms of the Riemann-Liouville integral [3].
Biography: Fatma Al-Musalhi is an Omani mathematician, who studied at Sultan Qaboos University between 2006 and 2017 for her bachelor's, master's, and PhD. She has worked in the same university since then: firstly at the Centre of Preparatory Studies from 2019 to 2022, where she was awarded Best Researcher, and then as a full faculty member of the Department of Mathematics since 2023. Her research interests are in fractional differential equations and mathematical modelling of infectious diseases. She has published more than 10 research papers in indexed journals and presented at international conferences in Bulgaria, Finland, etc. She also serves as a peer reviewer for several high-level journals.
Bibliography
[1] Al-Musalhi, F., Al-Salti, N., Karimov, E.: Initial boundary value problems for a fractional differential equation with hyper-Bessel operator. Fract. Calc. Appl. Anal. 21(1), 200–219 (2018). DOI: 10.1515/fca-2018-0013.
[2] Al-Musalhi, F., & Fernandez, A.: Fractional differential equations involving Erd´elyi-Kober derivatives with variable coefficients. Fract. Calc. and Appl. Anal., 1-30(2025).
[3] Fernandez, A., Restrepo, J.E., Suragan, D.: On linear fractional differential equations with variable coefficients. Appl. Math. Comput. 432, 127370 (2022)
[4] Al-Saqabi, B., Kiryakova, V.S.: Explicit solutions of fractional integral and differential equations involving Erd´elyi–Kober operators. Appl. Math. Comput. 95(1), 1–13 (1998)
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