A non-local problem with discontinuous matching condition for loaded mixed type equation involving the Caputo fractional derivative

Advances in Difference Equations

Obidjon Khayrullayevich Abdullaev¹  Kishin Sadarangani² 

[1] National University of Uzbekistan, Tashkent, Uzbekistan;University of Las-Palmas de Gran Canaria, Las Palmas, Spain

关键词: loaded equation;    parabolic-hyperbolic type;    Caputo fractional derivative;    existence and uniqueness of solution;    non-local condition;    discontinuous matching condition;    integral energy;    integral equations;    35M10;   

DOI  :  10.1186/s13662-016-0969-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This research work is devoted to investigations of the existence and uniqueness of the solution of a non-local boundary value problem with discontinuous matching condition for the loaded equation. Considering parabolic-hyperbolic type equations involves the Caputo fractional derivative and loaded part joins in Riemann-Liouville integrals. The uniqueness of a solution is proved by the method of integral energy and the existence is proved by the method of integral equations.

【 授权许可】

CC BY