Abstract
This paper deals with a time-fractional Fokker–Planck equation, where the time-fractional derivative (denoted by \(_{H}{\textrm{D}}_{a,t}^{1-\alpha }u\)) is in the Hadamard sense with order \(\alpha \in (0,1)\). With the help of the modified Laplace transform and its inverse transform, the mild solutions of the considered equation are constructed. The existence and uniqueness of the mild solutions are proved by the contraction mapping principle, and some regularity estimates are satisfied. For \(\alpha \in (1/2,1)\), the mild solution is shown to be the classical solution. The decay estimates of the solution u and \(_{H}{\textrm{D}}_{a,t}^{1-\alpha }u\) are also investigated.
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Wang, Z., Sun, L. Mathematical Analysis of the Hadamard-Type Fractional Fokker–Planck Equation. Mediterr. J. Math. 20, 245 (2023). https://doi.org/10.1007/s00009-023-02445-8
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DOI: https://doi.org/10.1007/s00009-023-02445-8