Well-posedness of the initial-boundary value problems for the time-fractional degenerate diffusion equations
Бөлшек реттi туындылы өзгешеленген диффузия теңдеулерi үшiн бастапқы шеттiк есептiң қисындылығы
Корректность начально-краевых задач для дробных вырожденных диффузионных уравнений
Smadiyeva A.G.
2022E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2022#107Issue 3145 - 151 pp.
This paper deals with the solving of initial-boundary value problems for the one-dimensional linear time-fractional diffusion equations with time-degenerate diffusive coefficients tβ with β > 1 − α. The solutions to initial-boundary value problems for the one-dimensional time-fractional degenerate diffusion equations with Riemann-Liouville fractional integral I0+1−, tα of order α ∈ (0, 1) and with Riemann-Liouville fractional derivative D0+α, t of order α ∈ (0, 1) in the variable, are shown. The solutions to these fractional diffusive equations are presented using the Kilbas-Saigo function Eα, m, l(z). The solution to the problems is discovered by the method of separation of variables, through finding two problems with one variable. Rather, through finding a solution to the fractional problem depending on the parameter t, with the Dirichlet or Neumann boundary conditions. The solution to the Sturm-Liouville problem depends on the variable x with the initial fractional-integral Riemann-Liouville condition. The existence and uniqueness of the solution to the problem are confirmed. The convergence of the solution was evidenced using the estimate for the Kilbas-Saigo function Eα, m, l(z) from and by Parsevals identity.
Kilbas-Saigo function , method of separation variables , time-fractional diffusion equation
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Al-Farabi Kazakh National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
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