Abstract
We consider the initial-boundary value problem on a half-line for the evolution equation with a fractional Abel type derivative and a fractional Caputo derivative Here is the modified Riesz potential and is the Riemann–Liouville fractional derivative. We study traditionally important problems of the theory of partial differential equations (PDEs), such as the existence and the uniqueness of the solution. We propose a new method for finding a solution. Also we get a closed form of the solution.
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