Abstract:
A nonlocal problem is investigated for the partial differential equation (diffusion equation of fractional order) in a finite domain. The boundary condition contains a linear combination of generalized operators of fractional integro-differentiation used on the solution in the characteristics and the solution and its derivative in the degenerating line. The uniqueness of the solution is proved by a modified Tricomi method. The existence of the solution is equivalently reduced to the question of the solvability of Fredholm integral equations of the second kind.
Keywords:
operator of fractional integro-differentiation, boundary value problem, Fredholm integral equation of the second kind.
Original article submitted 05/XI/2014 revision submitted – 11/I/2015
Citation:
O. A. Repin, A. V. Tarasenko, “Nonlocal problem for partial differential equations of fractional order”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:1 (2015), 78–86