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

RECOVERY OF A TIME-DEPENDENT SOURCE IN A FRACTIONAL LANGEVIN EQUATION Bakhodirjon Toshtemirov Kokand University, Uzbekistan. Email: [email protected] https://doi.org/10.5281/zenodo.15778222 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. Keywords: bi-ordinal Hilfer fractional derivative, Fourier-Legendre series, time-dependent inverse source problem