On a singular timefractional order wave equation with Bessel operator and Caputo derivative
Authors
Said Mesloub
 King Saud University, College of Science, Mathematics Department, P. O. Box 2455, Riyadh 11451, Saudi Arabia.
Imed Bachar
 King Saud University, College of Science, Mathematics Department, P. O. Box 2455, Riyadh 11451, Saudi Arabia.
Abstract
This paper deals with the study of the wellposedness 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.
Keywords
 Caputo derivative
 solvability of the problem
 fractional differential equation
 initial boundary value problem.
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