CAUCHY PROBLEMS FOR THE TIME-FRACTIONAL DEGENERATE DIFFUSION EQUATIONS

Borikhanov M.B. Smadiyeva A.G.
7 April 2023 al-Farabi Kazakh State National University

KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2023 #117 Issue 1 15 - 23 pp.

This paper is devoted to the Cauchy problems for the one-dimensional linear time-fractional diffusion equations with ∂t^α the Caputo fractional derivative of order α ∈ (0, 1) in the variable t and time-degenerate diffusive coefficients t^β with β > −α. The solutions of Cauchy problems for the one-dimensional time-fractional degenerate diffusion equations with the time-fractional derivative ∂t^α of order α ∈ (0, 1) in the variable t, are shown. In the Problem statement and main resultssection of the paper, the solution of the time-fractional degenerate diffusion equation in a variable coefficient with two different initial conditions are considered. In this work, a solution is found by using the Kilbas-Saigo function E_α,m,l (z) and applying the Fourier transform F and inverse Fourier transform F⁻¹ . Convergence of solution of problem 1 and problem 2 are proven using Plancherel theorem. The existence and uniqueness of the solution of the problem are confirmed.

Fourier transform , the Kilbas-Saigo function , Time-fractional diffusion equation

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Khoja Akhmet Yassawi International Kazakh–Turkish University Turkistan, Kazakhstan
Ghent University, Ghent, Belgium
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

Khoja Akhmet Yassawi International Kazakh–Turkish University Turkistan
Ghent University
Institute of Mathematics and Mathematical Modeling

10 лет помогаем публиковать статьи Международный издатель

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