A non-local problem for the Barenblatt-Zheltov-Kochina type fractional equations
This paper investigates a non-local problem associated with the fractional-order
Barenblatt–Zheltov–Kochina equation involving the Caputo fractional derivative. The non-local
problem under consideration is reduced to two auxiliary problems, and the solution of the
corresponding Cauchy problem is employed in the analysis. The existence and uniqueness theorems
are established for both the initial-boundary value problem. The results obtained extend the
theoretical framework of fractional differential equations and provide a foundation for further
theoretical developments as well as potential practical applications.
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