Approximations of Solutions to a Fractional Differential Equation with a Deviating Argument
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- Kumar, P., Pandey, D.N. & Bahuguna, D. Differ Equ Dyn Syst (2014) 22: 333. doi:10.1007/s12591-013-0188-0
In the present study, a fractional order differential equation with deviating argument is considered in a separable Hilbert space \(H\). We will prove the existence and convergence of an approximate solution for the given problem by using the analytic semigroup theory and the fixed point method. Finally, we consider the Faedo-Galerkin approximation of the solution and prove some convergence results.