Differential Equations and Dynamical Systems

, Volume 22, Issue 4, pp 333–352

Approximations of Solutions to a Fractional Differential Equation with a Deviating Argument

Original Research

DOI: 10.1007/s12591-013-0188-0

Cite this article as:
Kumar, P., Pandey, D.N. & Bahuguna, D. Differ Equ Dyn Syst (2014) 22: 333. doi:10.1007/s12591-013-0188-0

Abstract

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.

Keywords

Analytic semigroup Fractional order differential equation Banach fixed point theorem Faedo-Galerkin approximation 

AMS Subject Classification

34G10 34G20 34K30 35K90 47N20 47H06 

Copyright information

© Foundation for Scientific Research and Technological Innovation 2013

Authors and Affiliations

  • Pradeep Kumar
    • 1
  • Dwijendra N. Pandey
    • 2
  • D. Bahuguna
    • 1
  1. 1.Department of Mathematics and StatisticsIndian Institute of Technology KanpurKanpurIndia
  2. 2.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia

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