Initial–boundary value problem for diffusion equation involving time-space nonlocal operators
DOI:
https://doi.org/10.70474/mdyf4e09Keywords:
diffusion equation, fractional derivative, integral equation, involution, nonlocal Laplace operatorAbstract
This article studies a time-fractional diffusion equation with a space-nonlocal operator in a bounded domain. The fractional operators are defined using the Caputo derivative of order β and the Riemann–Liouville integral of order α, where 0<α<β≤1. The solution is represented as a series involving the two-parameter Mittag–Leffler function and orthonormal eigenfunctions of a Sturm–Liouville operator. The convergence of this series is analyzed, and sufficient conditions are obtained to ensure that the solution belongs to the required function space. Moreover, the uniqueness of the solution is proved, and its continuity in the domain follows from the uniform convergence of the series.
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