“YANGI AVLOD ILMIY TADQIQOTLARI” respublika ilmiy-amaliy konferensiyasi
EXISTENCE AND UNIQUENESS OF A SOLUTION TO A BITSADZE-SAMARSKII PROBLEM FOR A SUB-DIFFUSION EQUATION WITH THE REGULARIZED PRABHAKAR FRACTIONAL DERIVATIVE
Fergana State University
This paper investigates the unique solvability of a Bitsadze-Samarskii problem for a sub-diffusion equation involving the regularized Prabhakar fractional derivative. By deriving the solution of the corresponding first boundary value problem, the nonlocal problem is reduced to a Volterra integral equation of the second kind. The continuity of the kernel and the right-hand side ensures the existence of a unique solution to the integral equation. Consequently, the solution of the Bitsadze-Samarskii problem is represented through the solutions of the associated Volterra integral equation and the first boundary value problem. An existence and uniqueness theorem is established.