| Issue |
Math. Model. Nat. Phenom.
Volume 14, Number 3, 2019
Fractional order mathematical models in physical sciences
|
|
|---|---|---|
| Article Number | 312 | |
| Number of page(s) | 15 | |
| DOI | https://doi.org/10.1051/mmnp/2019014 | |
| Published online | 27 May 2019 | |
Initial-boundary value problems for a time-fractional differential equation with involution perturbation
1
Department of Mathematics, Sultan Qaboos University,
P.O. Box 36, Al-Khoud 123,
Muscat, Oman.
2
FracDiff Research Group (DR/RG/03), Sultan Qaboos University,
Muscat, Oman.
3
LaSIE, Faculté des Sciences et Technologies, Université de La Rochelle,
Avenue Michel Crépeau,
17000
La Rochelle, France.
* Corresponding author: mokhtar.kirane@univ-lr.fr
Received:
10
October
2018
Accepted:
2
March
2019
Direct and inverse initial-boundary value problems of a time-fractional heat equation with involution perturbation are considered using both local and nonlocal boundary conditions. Results on existence of formal solutions to these problems are presented. Solutions are expressed in a form of series expansions using appropriate orthogonal basis obtained by separation of variables. Convergence of series solutions are obtained by imposing certain conditions on the given data. Uniqueness of the obtained solutions are also discussed. The obtained general solutions are illustrated by an example using an appropriate choice of the given data.
Mathematics Subject Classification: 35R30 / 34A08 / 39B52
Key words: Initial-boundary value problems / time-fractional differential equation / involution perturbation
© EDP Sciences, 2019
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