On the Cauchy problems for Barenblatt-Zheltov-Kochina type fractional equations
In this article, the Cauchy problem for a homogeneous fractional-order equation of the
Barenblatt–Zheltov–Kochina type with the Caputo derivative is studied. The existence of a solution
to the given Cauchy problem is demonstrated using the Fourier method, and the continuity of
the obtained solution is proved by employing the properties of functional series. Furthermore, the
uniqueness of the solution is established. The properties of the Mittag-Leffler function are extensively
used in the process of proving the existence and uniqueness of the solution to the proposed problem.
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