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Solvability of the boundary-value problem for a mixed equation involving hyper-Bessel fractional differential operator and bi-ordinal Hilfer fractional derivative |
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| Authors: | Erkinjon Karimov Michael Ruzhansky Bakhodirjon Toshtemirov |
| Affiliation: | 1. V.I.Romanovskiy Institute of Mathematics, Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan;2. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium School of Mathematical Sciences, Queen Mary University of London, London, UK |
| Abstract: | In a rectangular domain, a boundary-value problem is considered for a mixed equation with a regularized Caputo-like counterpart of hyper-Bessel differential operator and the bi-ordinal Hilfer's fractional derivative. By using the method of separation of variables a unique solvability of the considered problem has been established. Moreover, we have found the explicit solution of initial-boundary problems for the heat equation with the regularized Caputo-like counterpart of the hyper-Bessel differential operator with the non-zero starting point. |
| Keywords: | bi-ordinal Hilfer's derivative boundary-value problems fractional wave equation hyper-Bessel fractional differential operator sub-diffusion equation |