Interval Solutions of Fractional Integro-differential Equations by Using Modified Adomian Decomposition Method

Abstract

This chapter explores the behavior of the estimated solution of the Caputo fractional Volterra–Fredholm integro-differential equation (CFVFIDE) in an uncertain environment (UE) by using a modified Adomian decomposition method (MADM). In this case, the uncertainty has been treated as an interval in the initial condition. It should be mentioned that in crisp/exact circumstances, the stated integral equation (IE) has been solved by multiple researchers using various approaches. The starting condition’s interval form is converted to a parametric form, which is then utilized to solve the integral problem. Corresponding results are included, and the validation has been done by comparing in special cases.