Well posedness for a singular two dimensional fractional initial boundary value problem with Bessel operator involving boundary integral conditions

Said Mesloub; Faten Aldosari; Said Mesloub; Faten Aldosari

doi:10.3934/math.2021569

AIMS Mathematics

2021, Volume 6, Issue 9: 9786-9812. doi: 10.3934/math.2021569

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Research article

Well posedness for a singular two dimensional fractional initial boundary value problem with Bessel operator involving boundary integral conditions

Said Mesloub ^,,
Faten Aldosari

Department of Mathematics, King Saud University University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 08 December 2020 Accepted: 08 June 2021 Published: 29 June 2021
MSC : 35D35, 35L20

This paper studies the existence and uniqueness of solutions of a non local initial boundary value problem of a singular two dimensional nonlinear fractional order partial differential equation involving the Caputo fractional derivative by employing the functional analysis. We first establish for the associated linear problem a priori estimate and prove that the range of the operator generated by the considered problem is dense. The technique of obtaining the a priori bound relies on the construction of a suitable multiplicator. From the resulted a priori estimate, we can establish the solvability of the associated linear problem. Then, by applying an iterative process based on the obtained results for the associated linear problem, we establish the existence, uniqueness and continuous dependence of the weak solution of the considered nonlinear problem.
- fractional differential equation,
- boundary integral condition,
- singular initial boundary value problem,
- well posedness,
- iterative process,
- bessel operator
Citation: Said Mesloub, Faten Aldosari. Well posedness for a singular two dimensional fractional initial boundary value problem with Bessel operator involving boundary integral conditions[J]. AIMS Mathematics, 2021, 6(9): 9786-9812. doi: 10.3934/math.2021569

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Abstract

This paper studies the existence and uniqueness of solutions of a non local initial boundary value problem of a singular two dimensional nonlinear fractional order partial differential equation involving the Caputo fractional derivative by employing the functional analysis. We first establish for the associated linear problem a priori estimate and prove that the range of the operator generated by the considered problem is dense. The technique of obtaining the a priori bound relies on the construction of a suitable multiplicator. From the resulted a priori estimate, we can establish the solvability of the associated linear problem. Then, by applying an iterative process based on the obtained results for the associated linear problem, we establish the existence, uniqueness and continuous dependence of the weak solution of the considered nonlinear problem.

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