A NON-LOCAL PROBLEM WITH DISCONTINUOS GLUING CONDITION FOR A LOADED WAVE-DIFFUSION EQUATION INVOLVES FRACTIONAL DERIVATIVE.
Abstract
In this work an existence and uniqueness of solution of non-local boundary
value problem with discontinuous matching condition for the loaded parabolic-hyperbolic
equation involving the Riemann-Liouville fractional derivative have been investigated. The
uniqueness of solution is proved by the method of integral energy and the existence is proved
by the method of integral equations.
Keywords
Loaded equation, wave-diffusion equation, Riemann-Liouville fractional derivative, existence and uniqueness of solution, non-local condition, discontinuous matching condition, integral energy, integral equations..
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