Inverse Boundary Value Problem for a Fractional Differential Equations of Mixed Type with Integral Redefinition Conditions
| Autor: | T. K. Yuldashev, B. J. Kadirkulov |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Hilfer operator
Differential equation General Mathematics 01 natural sciences Domain (mathematical analysis) Article 010305 fluids & plasmas classical solution symbols.namesake Mittag-Leffler function 0103 physical sciences mixed type equation Boundary value problem Uniqueness 0101 mathematics Fourier series Mathematics parameters Partial differential equation 010102 general mathematics Mathematical analysis Inverse problem symbols inverse problem solvability |
| Zdroj: | Lobachevskii Journal of Mathematics |
| ISSN: | 1818-9962 1995-0802 |
| Popis: | In this paper, we consider an inverse boundary value problem for a mixed type partial differential equation with Hilfer operator of fractional integro-differentiation in a positive rectangular domain and with spectral parameter in a negative rectangular domain. The differential equation depends from another positive parameter in mixed derivatives. With respect to first variable this equation is a fractional-order nonhomogeneous differential equation in the positive part of the considering segment, and with respect to second variable is a second-order differential equation with spectral parameter in the negative part of this segment. Using the Fourier series method, the solutions of direct and inverse boundary value problems are constructed in the form of a Fourier series. Theorems on the existence and uniqueness of the problem are proved for regular values of the spectral parameter. It is proved the stability of the solution with respect to redefinition functions, and with respect to parameter given in mixed derivatives. For irregular values of the spectral parameter, an infinite number of solutions in the form of a Fourier series are constructed. |
| Databáze: | OpenAIRE |
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