Differential Equations and Dynamical Systems

, Volume 22, Issue 4, pp 333–352 | Cite as

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

Original Research
First Online:

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 
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Notes

Acknowledgments

We highly appreciate the valuable suggestions and comments of the referees on our manuscript which helped to considerably improve the quality of the manuscript. The third author would like to acknowledge the financial aid from the Department of Science and Technology, New Delhi, under its research project SR/S4/MS:796.

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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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