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Green's Function Framework for Boundary Value Problems with the Regularized Prabhakar Fractional Derivative

Erkinjon KarimovDepartment of Mathematics: Analysis, Logics and Discrete Mathematics , Ghent University , Krijgslaan 297 , S8 , Ghent 9000 , BelgiumDoniyor UsmonovDepartment of Mathematical Analysis and Differential Equations , Fergana State University , Murabbiylar Str. 19 , 150100 Fergana , UzbekistanMaftuna MirzaevaDepartment of Mathematical Analysis and Differential Equations , Fergana State University , Murabbiylar Str. 19 , 150100 Fergana , Uzbekistan

ArXiv.orgrepository2026

ABI

Annotatsiya

In this work, the first initial-boundary value problem for a sub-diffusion equation involving the regularized Prabhakar fractional derivative is studied. The problem is solved by reducing it to two initial-boundary value problems using the superposition method. An explicit representation of the solution and the corresponding Green's function is obtained. The explicit form of the Green's function is expressed in terms of a bivariate Mittag-Leffler type function. Then, it is proved that the obtained solution indeed constitutes the solution of the considered problem.

Mavzular

Fractional Differential Equations Solutions Nonlinear Differential Equations Analysis Differential Equations and Boundary Problems

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