Generalized Monotone Iterative Method for Caputo Fractional Integro-differential Equation
Keywords:Caputo fractional integro-differential equation, linear integro-differential equations
AbstractUsing coupled lower and upper mathematical solutions we develop the generalized monotone iterative technique to solve Caputo fractional integro-differential equation of order q with periodic boundary condition, via initial value problem (IVP) where $0<q<1.$ We construct monotone iterates which are solutions of initial value problems associated with linear integro-differential equations, that are easier to obtain. In fact, we have obtained the explicit mathematical solution of the linear IVP of Caputo fractional integro-differential equation. We show that these iterates converge uniformly and monotonically to coupled minimal and maximal solutions of the problem considered here.
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