Abstract:
For a differential equation involving a fractional order diffusion equations, we study a non-local problem in an unbounded domain where the boundary condition involves a linear combination of generalized operators of a fractional integro-differentiation.
For various values of the parameters of these operators by Tricomi method we prove the uniqueness of solution to the considered problem. The existence of solution is obtained in the closed form as a solution to the appropriate equation with fractional derivative of various order.
Keywords:
boundary value problem, generalized operator of fractional integro-differentiation, Wright's function, fractional order differential equation.
Citation:
O. A. Repin, “Boundary value problem for partial differential equation with fractional Riemann–Liouville derivative”, Ufa Math. J., 7:3 (2015), 67–72
\Bibitem{Rep15}
\by O.~A.~Repin
\paper Boundary value problem for partial differential equation with fractional Riemann--Liouville derivative
\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 3
\pages 67--72
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\crossref{https://doi.org/10.13108/2015-7-3-67}
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Linking options:
https://www.mathnet.ru/eng/ufa291
https://doi.org/10.13108/2015-7-3-67
https://www.mathnet.ru/eng/ufa/v7/i3/p70
This publication is cited in the following 9 articles:
M. Kh. Ruziev, R. T. Zunnunov, N. T. Yuldasheva, G. B. Rakhimova, “Bitsadze-Samarskii type problem for the diffusion equation and degenerate hyperbolic equation”, Vestnik KRAUNTs. Fiz.-mat. nauki, 48:3 (2024), 33–42
R. R. Ashurov, R. T. Zunnunov, “An Analog of the Tricomi Problem for a Mixed-Type Equation with Fractional Derivative. Inverse Problems”, Lobachevskii J Math, 44:8 (2023), 3225
Ruziev M., “A Boundary Value Problem For a Partial Differential Equation With Fractional Derivative”, Fract. Calc. Appl. Anal., 24:2 (2021), 509–517
K. U. Khubiev, “Kraevaya zadacha dlya nagruzhennogo giperbolo-parabolicheskogo uravneniya s vyrozhdeniem poryadka”, Materialy IV Mezhdunarodnoi nauchnoi konferentsii “Aktualnye problemy prikladnoi matematiki”. Kabardino-Balkarskaya respublika, Nalchik, Prielbruse, 22–26 maya 2018 g. Chast III, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 167, VINITI RAN, M., 2019, 112–116
O. A. Repin, “Boundary-value problem with Saigo operatos for mixed type equation with fractional derivative”, Russian Math. (Iz. VUZ), 62:1 (2018), 70–75
O. A. Repin, “On a problem for mixed-type equation with fractional derivative”, Russian Math. (Iz. VUZ), 62:8 (2018), 38–42
K. U. Khubiev, “Zadachi so smescheniem dlya nagruzhennogo uravneniya giperbolo-parabolicheskogo tipa s operatorom drobnoi diffuzii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:1 (2018), 82–90
O. A. Repin, A. V. Tarasenko, “Ob odnoi zadache dlya uravneniya smeshannogo tipa s chastnoi drobnoi proizvodnoi Rimana–Liuvillya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:4 (2016), 636–643
O. A. Repin, A. A. Frolov, “On a Boundary Value Problem For An Equation of Mixed Type With a Riemann-Liouville Fractional Partial Derivative”, Differ. Equ., 52:10 (2016), 1384–1388
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