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International Journal of Differential Equations
Volume 2016, Article ID 9815796, 6 pages
http://dx.doi.org/10.1155/2016/9815796
Research Article

About a Problem for Loaded Parabolic-Hyperbolic Type Equation with Fractional Derivatives

1Department of Functional Analysis and Integral Equations, University of Las Palmas de Gran Canaria, Campus de Tafira Baja, Las Palmas, 35017 Gran Canaria, Spain
2Faculty of Mechanics-Mathematics, Department of Differential Equations and Mathematical Physics, National University of Uzbekistan, Universitetskaya 4, Almazar, 100125 Tashkent, Uzbekistan

Received 12 February 2016; Revised 7 June 2016; Accepted 29 June 2016

Academic Editor: Nikolai A. Kudryashov

Copyright © 2016 Kishin B. Sadarangani and Obidjon Kh. Abdullaev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An existence and uniqueness of solution of local boundary value problem with discontinuous matching condition for the loaded parabolic-hyperbolic equation involving the Caputo fractional derivative and Riemann-Liouville integrals have been investigated. The uniqueness of solution is proved by the method of integral energy and the existence is proved by the method of integral equations. Let us note that, from this problem, the same problem follows with continuous gluing conditions (at ); thus an existence theorem and uniqueness theorem will be correct and on this case.