On a singular time-fractional order wave equation with Bessel operator and Caputo derivative
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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.
Share and Cite
ISRP Style
Said Mesloub, Imed Bachar, On a singular time-fractional order wave equation with Bessel operator and Caputo derivative , Journal of Nonlinear Sciences and Applications, 10 (2017), no. 1, 60--70
AMA Style
Mesloub Said, Bachar Imed, On a singular time-fractional order wave equation with Bessel operator and Caputo derivative . J. Nonlinear Sci. Appl. (2017); 10(1):60--70
Chicago/Turabian Style
Mesloub, Said, Bachar, Imed. "On a singular time-fractional order wave equation with Bessel operator and Caputo derivative ." Journal of Nonlinear Sciences and Applications, 10, no. 1 (2017): 60--70
Keywords
- Caputo derivative
- solvability of the problem
- fractional differential equation
- initial boundary value problem.
MSC
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