Modified homotopy methods for generalized fractional perturbed Zakharov–Kuznetsov equation in dusty plasma

Abstract We propose a new modification of homotopy perturbation method (HPM) called the δ -homotopy transform ( -HPTM). This consists Laplace method, HPM, and control parameter . convergence in this helps adjusting controlling region series solution overcome some limitations HPM HPTM. The -HPTM q-homotopy analysis (q-HATM) are considered to study generalized time-fractional perturbed $(3+1)$ ( 3 + 1 ) -dimensional Zakharov–Kuznetsov equation with Caputo fractional time derivative. describes nonlinear dust-ion-acoustic waves magnetized two-ion-temperature dusty plasmas. selection an appropriate value auxiliary parameters n ħ q-HATM gives guaranteed solution, but difference between two techniques is that embedding p varies from zero nonzero , whereas q $\frac{1}{n}, n\geq{1}$ n , ≥ examine effect order on problem present error estimate when compared exact solution. outcomes reveal complete reliability efficiency proposed algorithm for solving various types physical models arising sciences engineering. Furthermore, we methods.