A NON-LOCAL PROBLEM WITH DISCONTINUOS GLUING CONDITION FOR A LOADED WAVE-DIFFUSION EQUATION INVOLVES FRACTIONAL DERIVATIVE. (International Scientific Journal Alfraganus, 2026)
In this work an existence and uniqueness of solution of non-local boundaryvalue problem with discontinuous matching condition for the loaded parabolic-hyperbolicequation involving the Riemann-Liouville fractional derivative have been investigated. Theuniqueness of solution is proved by the method of integral energy and the existence is provedby 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..