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R.Ashurov:Inverse Problem of Determining the Order of Fractional Derivative in Partial Derivative Eq

Date: Friday, 20 September, 2024 - 15:00 to 16:00 CEST Title : Inverse Problems of Determining the Order of Fractional Derivatives in Partial Derivative Equations Speaker : Ravshan Ashurov, Institute of Mathematics, Academy of Science of Uzbekistan, Tashkent, Uzbekistan Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy Organizers : Pavan Pranjivan Mehta* and Arran Fernandez** * SISSA, International School of Advanced Studies, Italy ** Eastern Mediterranean University, Northern Cyprus Keywords: Inverse problems, Partial differential equations, Initial-boundary value problems Abstract Determining the unknown order of a fractional derivative in differential equations modeling various processes is an important problem in modern applied mathematics. Inverse problems of determining these unknown parameters are not only of theoretical interest, but are also necessary for finding a solution to an initial-boundary value problem and studying the properties of solutions. In the last decade, this problem has been actively studied by many specialists. A number of interesting results have been obtained that have a certain applied significance. This report will give a brief overview of the most interesting works in this area, and will also consider methods for solving such inverse problems for equations of mathematical physics. Biography Professor Ravshan Ashurov is currently head of laboratory at the Institute of Mathematics of the Academy of Science of Uzbekistan. He studied at Moscow State University, receiving his PhD from there in 1982 and a Doctor of Science also from there in 1992. He has worked as a scientific researcher or visiting scientist at a number of institutions including Birmingham University in England, Vanderbilt University in the US, and the ICTP in Trieste. He has published more than 100 scientific papers as well as several books and monographs in English, Russian, and Uzbek. His research interests include fractional differential equations of ordinary and partial type, spectral theory of differential and pseudo-differential operators, harmonic analysis, and wavelet transforms. Bibliography [1] S. Alimov and R. Ashurov. “Inverse problem of determining an order of the Caputo time-fractional derivative for a subdiffusion equation”. In: Journal of Inverse Ill-posed Problems 28.5 (2020), pp. 651–658. [2] S. Alimov and R. Ashurov. “Inverse problem of determining an order of the Riemann-Liouville time-fractional derivative”. In: Progress in Fractional Differentiation and Applications 8 (2022), pp. 1–8. [3] R. Ashurov and Y. Fayziev. “Determination of fractional order and source term in subdiffusion equations”. In: Eurasian Mathematical Journal 13.1 (2021), pp. 19–31. [4] R. Ashurov and I. Sulaymonov. “Determining the order of time and spatial fractional derivatives”. In: Mathematical Methods in the Applied Sciences (2024). [5] R. Ashurov and R. Zunnunov. “Initial-boundary value and inverse problems for sub-diffusion equation in RN ”. In: Fractional Differential Calculus 10.2 (2020), pp. 291–306. [6] R. Ashurov and R. Zunnunov. “The inverse problem of determining the order of the fractional derivative in equations of mixed-type”. In: Lobachevskii Journal of Mathematics 42.12 (2021), pp. 2714–2729. [7] R.R. Ashurov and Y. Fayziev. “Uniqueness and existence for inverse problem of determining an order of time-fractional derivative of subdiffusion equation”. In: Lobachevskii Journal of Mathematics 42.3 (2021), pp. 508–516. [8] R.R. Ashurov and O. Mukhiddinova. “Inverse problem of determining the order of the fractional derivative in the Rayleigh–Stokes equation”. In: Fractional Calculus and Applied Analysis 26 (2023), pp. 1691–1708. [9] R.R. Ashurov and S. Sitnik. “Identification of the Order of the Fractional Derivative for the Fractional Wave Equation”. In: Fractal and Fractional 7 (2023), p. 67. [10] R.R. Ashurov and S.R. Umarov. “Determination of the order of fractional derivative for subdiffusion equations”. In: Fractional Calculus and Applied Analysis 23.6 (2020), pp. 1647–1662