INITIAL–BOUNDARY VALUE PROBLEMS TO THE TIME–SPACE NONLOCAL DIFFUSION EQUATION
Borikhanov M.B. Mambetov S.A.
June 2024Element D.O.O.
Fractional Differential Calculus
2024#14Issue 1101 - 108 pp.
This article investigates a time-fractional space-nonlocal diffusion equation in a bounded domain. The fractional operators are defined rigorously, using the Caputo fractional derivative of order β and the Riemann-Liouville fractional integral of order α, where 0 < α < β ≤ 1. The solution is expressed as a series involving the two-parameter Mittag-Leffler function and orthonormal eigenfunctions of the Sturm-Liouville operator. The convergence of the series is investigated, and conditions for the solution to belong to a specific function space are established. The uniqueness of the solution is demonstrated and the continuity of the solution in the specified domain is confirmed through the uniform convergence of the series.
and phrases: Fractional derivative , integral equation , the method of separation variables , time-space nonlocal diffusion equation
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Khoja Akhmet Yassawi International Kazakh–Turkish University, Sattarkhanov ave., 29, Turkistan, 161200, Kazakhstan
Institute of Mathematics and Mathematical Modeling, 125 Pushkin str, Almaty, 050010, Kazakhstan
Al–Farabi Kazakh National University, Al–Farabi ave. 71, Almaty, 050040, Kazakhstan
Khoja Akhmet Yassawi International Kazakh–Turkish University
Institute of Mathematics and Mathematical Modeling
Al–Farabi Kazakh National University
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