ON A TIME-NONLOCAL BOUNDARY VALUE PROBLEM
FOR TIME-FRACTIONAL PARTIAL
E. Karimov1, B. Toshtemirov2 1 Fergana State University
Fergana - 150100, UZBEKISTAN
V. I. Romanovskiy Institute of Mathematics
Tashkent - 100174, UZBEKISTAN 2 V. I. Romanovskiy Institute of Mathematics,
Tashkent - 100174, UZBEKISTAN
Ghent - 9000, BELGIUM
A boundary value problem with a nonlocal m-point condition in time for a space-degenerate partial differential equation involving the bi-ordinal Hilfer fractional derivative is the main subject of the present investigation. We aim to prove a unique solvability of this problem based on certain properties of the Legendre polynomials and the two-parameter Mittag-Leffler function. An explicit solution to the considered problem is found in the form of the Fourier-Legendre series.
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