Extended Laplace Power Series Method for Solving Nonlinear Caputo Fractional Volterra Integro-Differential Equations

In this paper, we compile the fractional power series method and Laplace transform to design a new algorithm for solving Volterra integro-differential equation. For that, assume (LPS) solution in terms of q=1m,m∈Z+, where derivative order α=qγ, which γ∈Z+. This assumption will help us write integral, kernel, nonhomogeneous as LPS with same power. The recurrence relations finding coefficients can be constructed using form. To demonstrate algorithm’s accuracy, residual error is defined calculated several values derivative. Two strongly nonlinear examples are discussed provide efficiency algorithm. gains powerful results kind problem. Under Caputo meaning symmetry order, obtained illustrated numerically graphically. Geometrically, behavior solutions declares that changing parameter their domain alters style these symmetric meaning, well indicates harmony symmetry, leads them fully coincide at value ordinary From simulations, report recommended novel straightforward, accurate, superb tool generate analytic-approximate integral equations order.