Non-local problems with integral gluing condition for loaded mixed type equations involving the Caputo fractional derivative. (English) Zbl 1383.35239

Abdullaev, Obidjon Kh.; Sadarangani, Kishin B.

Electron. J. Differ. Equ. 2016, Paper No. 164, 10 p. (2016).

Summary: In this work, we study the existence and uniqueness of solutions to non-local boundary value problems with integral gluing condition. Mixed type equations (parabolic-hyperbolic) involving the Caputo fractional derivative have loaded parts in Riemann-Liouville integrals. Thus we use the method of integral energy to prove uniqueness, and the method of integral equations to prove existence.

MSC:

35R11	Fractional partial differential equations
35A01	Existence problems for PDEs: global existence, local existence, non-existence
35A02	Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35C05	Solutions to PDEs in closed form
35C15	Integral representations of solutions to PDEs

Keywords:

Caputo fractional derivatives; loaded equation; non-local problem; integral gluing condition; existence; uniqueness