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Analytical solutions of incommensurate fractional differential equation systems with fractional order 1<α,β<2 via bivariate Mittag-Leffler functions
- Source :
- AIMS Mathematics, Vol 7, Iss 2, Pp 2281-2317 (2022)
- Publication Year :
- 2022
- Publisher :
- AIMS Press, 2022.
-
Abstract
- In this paper, we derive the explicit analytical solution of incommensurate fractional differential equation systems with fractional order $ 1 < \alpha, \beta < 2 $. The derivation is extended from a recently published paper by Huseynov et al. in [1], which is limited for incommensurate fractional order $ 0 < \alpha, \beta < 1 $. The incommensurate fractional differential equation systems were first converted to Volterra integral equations. Then, the Mittag-Leffler function and Picard's successive approximations were used to obtain the analytical solution of incommensurate fractional order systems with $ 1 < \alpha, \beta < 2 $. The solution will be simplified via some combinatorial concepts and bivariate Mittag-Leffler function. Some special cases will be discussed, while some examples will be given at the end of this paper.
- Subjects :
- incommensurate fractional order system
General Mathematics
bivariate mittag-leffler function
Bivariate analysis
picard's successive approximations
analytical solutions
Alpha (programming language)
QA1-939
Order (group theory)
Applied mathematics
Beta (velocity)
Fractional differential
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 7
- Issue :
- 2
- Database :
- OpenAIRE
- Journal :
- AIMS Mathematics
- Accession number :
- edsair.doi.dedup.....f879cff16ee87d1fc0079e4e3a345194