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A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on theR -function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations