Perturbation method for linear and non-linear fractional order systems and integral representation for evaluation of integrals

Arman Aghili; M. R. Masomi

doi:10.5269/bspm.v33i1.21411

Authors

Arman Aghili University of Guilan Faculty of Mathematical Sciences Applied Mathematics Department
M. R. Masomi University of Guilan Faculty of Mathematical Sciences Applied Mathematics Department

DOI:

https://doi.org/10.5269/bspm.v33i1.21411

Keywords:

Laplace transform, Ingegral representation, Caputo fractional derivative, Fractional differential equations, Perturbation method, Fractional difference equation

Abstract

In the present work, the authors used the Laplace transform - perturbation method to solve certain linear and non-linear systems of fractional differential and difference equations with constant coefficients with the fractional derivatives in the Caputo sense. We also considered the problems of string vibrations in different cases with fractional damping. Another purpose of this article is to evaluate certain integrals. Illustrative examples are also provided.