In this study, we provide the Aboodh decomposition method, a novel analytical technique. The fundamental definitions and theorems of suggested approach are provided analyzed. This new method is mixture transform Adomian method. used to solve nonlinear integro-differential equations (IDEs), solutions given as quickly expanding series terms. We compute maximum absolute error some figures compare ...

Fractional differential equations can model various complex problems in physics and engineering, but there is no universal method to solve fractional models precisely. This paper offers a new hope for this purpose by coupling the homotopy perturbation with Aboodh transform. The hybrid technique leads simple approach finding an approximate solution, which converges fast exact one less computing ...

The main goal of this paper is to introduce a new scheme, known as the Aboodh homotopy integral transform method (AHITM), for approximate solution wave problems in multi-dimensional orders. (AIT) removes restriction variables recurrence relation, whereas perturbation (HPM) derives successive iterations using initial conditions. convergence analysis provided study equation with multiple dimensio...

In this article, a hybrid method that combines Aboodh transform, variational iteration method, and the homotopyperturbation is presented for approximate solution of important partial differential equations describe wave like in one, two three dimensions. The suggested utilizes only initial conditions to providean analytical solution, contrast separation variables, also requires boundary conditi...

In this paper, the Aboodh transform is utilized to construct an approximate analytical solution for time-fractional Zakharov–Kuznetsov equation (ZKE) via Adomian decomposition method. context of a uniform magnetic flux, framework illustrates action weakly nonlinear ion acoustic waves in plasma carrying cold ions and hot isothermal electrons. Two compressive rarefactive potentials (density fract...

In this study, the highly accurate analytical Aboodh transform decomposition method (ATDM) in sense of Caputo fractional derivative is used to determine approximate and exact solutions both linear nonlinear time-fractional Schrodinger differential equations (SDEs) with zero nonzero trapping potential that describe nonrelativistic quantum mechanical activity. The Adomian (ADM) Caputo’s are combi...

In this study, we use a new approach, known as the Aboodh residual power series method (ARPSM), in order to obtain analytical results of Black–Scholes differential equations (BSDEs), which are prime for judgment European call and put options on non-dividend-paying stock, especially when they consist time-fractional derivatives. The fractional derivative is considered Caputo sense. This approach...