Non-local boundary value problem for a system of fractional partial differential equations of the type I

Murat O. Mamchuev; Murat O. Mamchuev

doi:10.3934/math.2020011

AIMS Mathematics

2020, Volume 5, Issue 1: 185-203. doi: 10.3934/math.2020011

Previous Article Next Article

Research article

Non-local boundary value problem for a system of fractional partial differential equations of the type I

Murat O. Mamchuev ^,

Institute of Applied Mathematics and Automation of KBSC of RAS, Shortanova str. 89-A, Nalchik, 360000, Kabardino-Balkar Republic, Russia

Received: 01 August 2019 Accepted: 18 October 2019 Published: 28 October 2019
MSC : 35A08, 35A09, 35C05, 35C15, 35F40, 35F45, 35F46, 35R11

A non-local boundary value problem in a rectangular domain for a system of fractional partial differential equations is investigated, in the case when all the eigenvalues of the matrix coefficient in the main part are sign-definite. Conditions for unique solvability of the problem under studying are obtained.
- fractional order derivatives,
- fractional hyperbolic systems,
- non-local boundary value problem,
- conditions for unique solvability
Citation: Murat O. Mamchuev. Non-local boundary value problem for a system of fractional partial differential equations of the type I[J]. AIMS Mathematics, 2020, 5(1): 185-203. doi: 10.3934/math.2020011

Related Papers:

Abstract

A non-local boundary value problem in a rectangular domain for a system of fractional partial differential equations is investigated, in the case when all the eigenvalues of the matrix coefficient in the main part are sign-definite. Conditions for unique solvability of the problem under studying are obtained.

References

[1]	A. M. Nakhushev, Fractional Calculus and Its Applications, Moscow: Fizmatlit, 2003.
[2]	P. Clement, G. Gripenberg, S. O. Londen, Schauder estimates for equations with fractional derivatives, T. Am. Math. Soc., 352 (2000), 2239-2260. doi: 10.1090/S0002-9947-00-02507-1
[3]	M. O. Mamchuev, Boundary value problem for a multidimensional system of equations with Riemann-Liouville fractional derivatives, Sib. Electron. Math. Rep., 16 (2019), 732-747.
[4]	P. Clement, G. Gripenberg, S. O. Londen, Hölder regularity for a linear fractional evolution equation, In: Topics in Nonlinear Analysis, Basel: Birkhäuser, 1999, 62-82.
[5]	A. V. Pskhu, Solution of a boundary value problem for a fractional partial differential equation, Differ. Eq., 39 (2003), 1150-1158. doi: 10.1023/B:DIEQ.0000011289.79263.02
[6]	A. V. Pskhu, Fractional Partial Differential Equations, Moscow: Nauka, 2005.
[7]	M. O. Mamchuev, A boundary value problem for a first-order equation with a partial derivative of a fractional order with variable coefficients, Reports of Adyghe (Circassian) International Academy of Sciences, 11 (2009), 32-35.
[8]	M. O. Mamchuev, Cauchy problem in non-local statement for first order equation with partial derivatives of fractional order with variable coefficients, Reports of Adyghe (Circassian) International Academy of Sciences, 11 (2009), 21-24.
[9]	M. O. Mamchuev, Boundary Value Problems for Equations and Systems with the Partial Derivatives of Fractional Order, Nalchik: Publishing house KBSC of RAS, 2013.
[10]	R. Gorenflo, A. Iskenderov, Y. Luchko, Mapping between solutions of fractional diffusion-wave equations, Fract. Calc. Appl. Anal., 3 (2000), 75-86.
[11]	V. F. Morales-Delgado, M. A. Taneco-Hern'andez, J. F. G'omez-Aguilar, On the solutions of fractional order of evolution equations, EPJ Plus, 132 (2017), 47.
[12]	M. O. Mamchuev, Boundary value problem for a system of fractional partial differential equations, Differ. Eq., 44 (2008), 1737-1749. doi: 10.1134/S0012266108120100
[13]	M. O. Mamchuev, Boundary value problem for a linear system of equations with the partial derivatives of fractional order, Chelyabinsk Phys. Math. J., 2 (2017), 295-311.
[14]	A. Heibig, Existence of solutions for a fractional derivative system of equations, Integr. Equat. Oper. Th., 72 (2012), 483-508. doi: 10.1007/s00020-012-1950-3
[15]	A. N. Kochubei, Fractional-parabolic systems, Potential Anal., 37 (2012), 1-30. doi: 10.1007/s11118-011-9243-z
[16]	A. N. Kochubei, Fractional-hyperbolic systems, Fract. Calc. Appl. Anal., 16 (2013), 860-873.
[17]	M. O. Mamchuev, Cauchy problem for the system of fractional partial equations of fractional order, Bulletin KRASEC. Phys. Math. Sci., 23 (2018), 76-82.
[18]	M. O. Mamchuev, Boundary value problems for a system of differential equations with partial derivatives of fractional order for unlimited domains, Reports of Adyghe (Circassian) International Academy of Sciences, 6 (2003), 64-67.
[19]	M. O. Mamchuev, Fundamental solution of a system of fractional partial differential equations, Differ. Eq., 46 (2010), 1123-1134. doi: 10.1134/S0012266110080069
[20]	M. O. Mamchuev, Cauchy problem in non-local statement for a system of fractional partial differential equations, Differ. Eq., 48 (2012), 354-361. doi: 10.1134/S0012266112030068
[21]	M. O. Mamchuev, Mixed problem for loaded system of equations with Riemann-Liouville derivatives, Math. Notes, 97 (2015), 412-222. doi: 10.1134/S0001434615030128
[22]	M. O. Mamchuev, Mixed problem for a system of fractional partial differential equations, Differ. Eq., 52 (2016), 133-138. doi: 10.1134/S0012266116010122
[23]	M. O. Mamchuev, Non-local boundary value problem for a system of equations with the partial derivatives of fractional order, Math. Notes NEFU, 26 (2019), 23-31.
[24]	E. M. Wright, On the coefficients of power series having exponential singularities, J. London Math. Soc., 8 (1933), 71-79.
[25]	E. M. Wright, The asymptotic expansion of the generalized Bessel function, Proc. London Math. Soc. Ser. II, 38 (1934), 257-270.
[26]	R. Gorenflo, Y. Luchko, F. Mainardi, Analytical properties and applications of the Wright function, Fract. Calc. Appl. Anal., 2 (1999), 383-414.

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)