On a nonlocal 1-D initial value problem for a singular fractional-order parabolic equation with Bessel operator

Advances in Difference Equations

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[1] 0000 0004 1773 5396, grid.56302.32, Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia;

关键词: Solvability of the problem;    Weighted integral conditions;    Fractional differential equation;    Initial boundary value problem;    35D35;    35L20;   

DOI  :  10.1186/s13662-019-2196-z

来源: publisher

【 摘 要 】

In this paper, we obtain some results of the existence and uniqueness of a generalized solution for a singular fractional initial boundary value problem in the Caputo sense subject to Neumann and weighted integral conditions. We show that a priori estimate or energy inequality methods can be successfully applied to obtaining a priori estimates for the solution of initial fractional boundary problems as in the classical case. The obtained results will contribute in the development of the functional analysis method and enrich the existing nonextensive literature on the nonlocal fractional mixed problems in the Caputo sense.

【 授权许可】

CC BY