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

Carl F. Lorenzo | Zendy; T. T. Hartley | Zendy; Rachid Malti | Zendy

Open Access

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

Author(s) -

Carl F. Lorenzo,

T. T. Hartley,

Rachid Malti

Publication year - 2013

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2012.0151

Subject(s) - mathematics , laplace transform , linear differential equation , trigonometry , fractional calculus , mathematical analysis , principal part , trigonometric functions , constant coefficients , differential equation , exponential function , geometry

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.

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