Study of composite fractional relaxation differential equation using fractional operators with and without singular kernels and special functions

[摘要] Our aim in this article is to solve the composite fractional relaxation differential equation by using different definitions of the non-integer order derivative operator$D_{t}^{\alpha }$ , more specifically we employ the definitions of Caputo, Caputo–Fabrizio and Atangana–Baleanu of non-integer order derivative operators. We apply the Laplace transform method to solve the problem and express our solutions in terms of Lorenzo and Hartley’s generalised G function. Furthermore, the effects of the parameters involved in the model are graphically highlighted.

[学科分类] 航空航天科学

[关键词] Fractional calculus;Composite fractional relaxation equation;Basset problem