On a singular time-fractional order wave equation with Bessel operator and Caputo derivative

Volume 10, Issue 1, pp 60--70 http://dx.doi.org/10.22436/jnsa.010.01.06

Publication Date: January 26, 2017 Submission Date: April 11, 2016

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Authors

Said Mesloub - Mathematics Department, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia. Imed Bachar - Mathematics Department, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.

Abstract

This paper deals with the study of the well-posedness of a mixed fractional problem for the wave equation defined in a bounded space domain. The fractional time derivative is described in the Caputo sense. We prove the existence and uniqueness of solution as well as its dependence on the given data. Our results develop and show the efficiency and effectiveness of the functional analysis method when we deal with fractional partial differential equations instead of the nonfractional equations which have been extensively studied by many authors during the last three decades.

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Keywords

• Caputo derivative
• solvability of the problem
• fractional differential equation
• initial boundary value problem.

MSC

•  35D35
•  35L20

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