RECOVERY OF A TIME-DEPENDENT SOURCE IN A FRACTIONAL LANGEVIN EQUATION



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Bakhodirjon Toshtemirov
Kokand University, Uzbekistan.

Abstract

In the current paper, we are interested in studying the time-dependent inverse source problem for the space-degenerate fractional Langevin-type PDE involving a bi-ordinal Hilfer fractional derivative. Sufficient conditions for the given data were established for the existence and uniqueness of the solution. The technique for showing the existence result is based on the uniform convergence of the series.

Foydalangan adabiyotlar

1. Stefanov, A. Vasy, M. Zworski, Inverse Problems and Applications, Amer Mathematical Society, -2014.
2. N. Blaunstein, V. Yakubov, Electromagnetic and Acoustic Wave Tomography: Direct and Inverse Problems in Practical Applications, Chapman and Hall/CRC, -2018.
3. A.S. Hendy, K. Van Bockstal, On a Reconstruction of a Solely Time-Dependent Source in a Time-Fractional Diffusion Equation with Non-smooth Solutions, J. Sci. Comput. -2022. -90, 41.
4. K. Sakamoto, M. Yamamoto, Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems, Journal of Mathematical Analysis and Applications, -2011, -Vol. 382(1), pp. 426-447,
5. M. Slodička, D. Lesnic, T.T.M. Onyango, Determination of a time-dependent heat transfer coefficient in a nonlinear inverse heat conduction problem, Inverse Problems in Science and Engineering, -2009. -Vol. 18(1). -P. 65-81.
6. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and applications of fractional differential equation, Elsevier, Amsterdam. -2006.
7. E. Karimov, B. Toshtemirov, On a time-nonlocal boundary value problem for time-fractional partial differential equation, International Journal of Applied Mathematics, -2022, Vol. 35(3), pp. 423-438. doi:10.12732/ijam.v35i3.5
8. Kaplan W. Advanced Calculus. 5th Edition. Pearson, -2002.

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Issue

Research Focus International Scientific Journal 4 (6)

Bo'lim

01.00.00 – Physics and mathematics sciences

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