Electron. J. Diff. Equ., Vol. 2016 (2016), No. 164, pp. 1-10.

Non-local problems with integral gluing condition for loaded mixed type equations involving the Caputo fractional derivative

Obidjon Kh. Abdullaev, Kishin B. Sadarangani

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.

Submitted April 8, 2016. Published June 28, 2016.
Math Subject Classifications: 34K37, 35M10.
Key Words: Caputo fractional derivatives; loaded equation; non-local problem; integral gluing condition; existence; uniqueness.

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Obidjon Kh. Abdullaev
Department of Differential equations and Mathematical Physics
National University of Uzbekistan
100114 Uzbekistan, Tashkent, Uzbekistan
email: obidjon.mth@gmail.com
  Kishin S. Sadarangani
Department of Mathematics
University of Las-Palmas de Gran Canaria
35017 Las Palmas, Spain
email: ksadaran@dma.ulpgc.es

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