Abstract
In this paper, we obtain an analytical solution for a system of multi-term linear fractional differential equations by using the analytic expression of inverse of multi-term fractional integral operator with matrix coefficients. The system of multi-term linear fractional differential equations is an efficient tool for solving the multi-term fractional partial differential equations. Firstly, several properties of multivariate Mittag–Leffler matrix function are given. Then, the reversibility of multi-term fractional integral operator with matrix coefficients and continuity of its inverse are proved, and the analytic expression of its inverse is obtained by the multivariate Mittag–Leffler matrix function. Finally, by using above results, the analytical solution for a system of multi-term linear fractional differential equations is presented, and some examples are shown to illustrate our results.
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Song-Guk Jong, Hui-Chol Choe and Yong-Do Ri. The first draft of the manuscript was written by Song-Guk Jong and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Conceptualization: Song-Guk Jong; Methodology: Song-Guk Jong, Hui-Chol Choe; Formal analysis and investigation: Song-Guk Jong; Writing - original draft preparation: Song-Guk Jong, Hui-Chol Choe; Supervision: Yong-Do Ri.
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Jong, SG., Choe, HC. & Ri, YD. A New Approach for an Analytical Solution for a System of Multi-term Linear Fractional Differential Equations. Iran J Sci Technol Trans Sci 45, 955–964 (2021). https://doi.org/10.1007/s40995-021-01099-z
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DOI: https://doi.org/10.1007/s40995-021-01099-z
Keywords
- Mittag–Leffler function
- Fractional differential equation
- Fractional integral operator
- Analytical solution