Solvability of the boundary‐value problem for a mixed equation involving hyper‐Bessel fractional differential operator and bi‐ordinal Hilfer fractional derivative
Erkinjon KarimovDepartment of Mathematical Analysis and Differential Equations Fergana State University Fergana UzbekistanMichael RuzhanskyDepartment of Mathematics: Analysis, Logic and Discrete Mathematics Ghent University Ghent BelgiumBakhodirjon ToshtemirovDepartment of Mathematics: Analysis, Logic and Discrete Mathematics Ghent University Ghent Belgium
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Аннотация
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.
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