Homotopy time-fractional enhancement soliton solution for six component complex cometary plasma with thermal heavy ions

Abstract

A dusty plasma system composed of three inertial species and three Kappa-distributed inertial-less species is considered. The hydrodynamic fluid equation used to describe investigated plasma system. The plasma system under consideration is a very rich system, so in this paper the effective Debye length and effective plasma frequency are considered to normalize all physical quantities. The Kortweg de-Veris equation is derived using the reductive perturbation method. Two envelope solitons (bright and dark) are propagating, and their appearance depends mainly on the values thermal parameter of heavy ions (oxygen ions) as well as the mass ratio for dust plasma. The homotopy perturbed transform method (HPTM) is used to solve the reduced time-fractional Korteweg-de Vries (TFKdV) equation. The effects of fractional parameters on the solution solutions are examined. Our results show that the shape of the solitary pulse is highly controlled by the fractional order, as well as the plasma parameters in addition to that the HPTM is very useful method, where few terms approximately three terms are enough to get successful approximate solution for fractional type equations.