Analysis of the non-linear higher dimensional fractional differential equations arising in dusty plasma using the Atangana–Baleanu fractional derivative - Attiya Nazneen; Rashid Nawaz; Laiq Zada; Nasir Ali; Mohamed Benghanem; Hijaz Ahmad (Results in Engineering)
In the present work, a relatively new derivative namely the Atangana–Baleanu fractional derivative is extended to derive an approximate solution to the non-linear higher dimensional fractional differential equations such as the Fractional perturbed Zakharov–Kuznetsov equation. The said model arises in many fields of physics and mathematics to model the dust-ion-acoustic waves in the magnetized two ion-temperature in the dusty plasmas. The methodology used for the simulation of the above model is the Adomian decomposition method and the derivative is considered as the Atangana–Baleanu fractional derivative in the Caputo's sense. The method has been successfully applied to the higher dimension fractional order Partial differential equations and some fruitful results have been achieved. The combination handles these types of equations appropriately and simply. The devised method yields the best approximate solutions shown numerically and graphically through tables and graphs respectively. Comparison of the absolute errors for different fractional orders confirms the efficiency, precision and convergence of the proposed method towards an exact solution in a few iterations.