Boundary value problem for the time-fractional wave equation
Уақыт бойынша бөлшек туындысы бар толқындық теңдеудiң шеткi есебi
Краевая задача для волнового уравнения с дробной производной по времени
Kosmakova M.T. Khamzeyeva A.N. Kasymova L.Z.
2024E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2024#114Issue 2124 - 134 pp.
In the article, the boundary value problem for the wave equation with a fractional time derivative and with initial conditions specified in the form of a fractional derivative in the Riemann-Liouville sense is solved. The definition domain of the desired function is the upper half-plane (x,t). To solve the problem, the Fourier transform with respect to the spatial variable was applied, then the Laplace transform with respect to the time variable was used. After applying the inverse Laplace transform, the solution to the transformed problem contains a two-parameter Mittag-Leffler function. Using the inverse Fourier transform, a solution to the problem was obtained in explicit form, which contains the Wright function. Next, we consider limiting cases of the fractional derivative’s order which is included in the equation of the problem.
Fourier transform , fractional derivative , Laplace transform , Mittag-Leffler function , Wright function
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Karaganda Buketov University, 28 Universitetskaya street, Karaganda, 100028, Kazakhstan
Karaganda Buketov University, 28 Universitetskaya street, Karaganda, 100028, Kazakhstan
Abylkas Saginov Karaganda Technical University, 56 Ave. Nursultan Nazarbayev, Karaganda, 100027, Kazakhstan
Karaganda Buketov University
Karaganda Buketov University
Abylkas Saginov Karaganda Technical University
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