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

• Published in: Advances in difference equations Vol. 2019; no. 1; pp. 1 - 14
• Main Authors: Mesloub, Said, Bachar, Imed
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 27.06.2019; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Boundary value problems; Difference and Functional Equations; Fractional differential equation; Functional Analysis; Initial boundary value problem; Mathematics; Mathematics and Statistics; Operators (mathematics); Ordinary Differential Equations; Partial Differential Equations; Solvability of the problem; Weighted integral conditions; Weighted integral conditions; Fractional differential equation; Solvability of the problem; Initial boundary value problem; 35D35; 35L20
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-019-2196-z

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.