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

作者：Sadarangani Kishin; Abdullaev Obidjon Khayrullayevich^*

来源：Advances in Difference Equations, 2016, 2016(1): 241.

DOI：10.1186/s13662-016-0969-1

• loaded equation
• parabolic-hyperbolic type
• Caputo fractional derivative
• existence and uniqueness of solution
• non-local condition
• discontinuous matching condition
• integral energy
• integral equations

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.

• 出版日期2016-9-22