Obidjon Kh. Abdullaev, Kishin B. Sadarangani
Abstract:
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 |
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| 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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