Fractional Differential Equations: An Approximate – Series Form Solution

Modern society faces many nonlinear problems, which nonlinear equations are better suited to understand and address them. Despite having access to high-performance digital computers, we still struggle to find precise and superior solutions to nonlinear problems, particularly the analytical approximation than its numerical consequence. The Aboodh transform iterative method, based on a new iterative method and the Aboodh transform, is the methodology we suggest in this thesis work to solve fractional differential equations, and the fractional order is taken into account by the Caputo operator. The technique combines the Aboodh transform with a fresh iterative approach to produce a series-form solution with easily calculatable components. The decomposition method is suited to visible issues, solve nonlinear problems without linearization, perturbation, or discretization methods, yet requiring less computational work than the traditional conventional methods, the numerical. The nonlinearity and linearity terms are decomposed in a series form. A few examples that are sufficiently backed up by numerical evidences have been provided to show the effectiveness of the scheme. The graphical solution showed how the fractional order of the scheme affected the results. In general, the solution profiles have demonstrated or shown that the scheme is almost exact and strength forward, simple to apply, and computationally less expensive. The solutions to the fractional differential equation’s exact problems are completely consistent with the findings, and the proposed scheme effectively and fully captures its true behavior and fractional effects.