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Solving coupled pairs of fractional differential equations by Mikusiński's operational calculus

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  • Mikusiński's operational calculus is an algebraic method for interpreting integro-differential operators and solving the corresponding equations. It has been a powerful method in fractional calculus, providing solutions for multi-term linear differential equations involving various fractional-order operators. Here, it is applied to general linear systems of two fractional differential equations involving Riemann–Liouville or Caputo derivatives of real or complex orders, and the solutions are found in terms of trivariate Mittag-Leffler functions.

    Mathematics Subject Classification: Primary: 44A40, 34A08; Secondary: 26A33, 33E12.

    Citation:

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  • [1] A. Ahmadova, I. T. Huseynov, A. Fernandez and N. I. Mahmudov, Trivariate Mittag-Leffler functions used to solve multi-order systems of fractional differential equations, Commun. Nonlin. Sci. Numer. Simul., 97 (2021), Paper No. 105735, 23 pp. doi: 10.1016/j.cnsns.2021.105735.
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