SOLVING COUPLED PAIRS OF FRACTIONAL DIFFERENTIAL EQUATIONS BY MIKUSINSKI'S OPERATIONAL CALCULUS

Abstract

Mikusi & nacute;ski'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.