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Generalized Monotone Iterative Method for Caputo Fractional Integro-differential Equations

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2016

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Abstract (2. Language): 
Using coupled lower and upper 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 easy to obtain. We show that these iterates converge uniformly and monotonically to coupled minimal and maximal solutions of the problem considered. We have obtained explicit solution of the linear IVP of Caputo fractional integro-differential equation
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