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

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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.

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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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Authors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur,  208016, India

    Pradeep Kumar & D. Bahuguna

  2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee,  247667, India

    Dwijendra N. Pandey

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  1. Pradeep Kumar
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  2. Dwijendra N. Pandey
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  3. D. Bahuguna
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Correspondence to Pradeep Kumar.

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Kumar, P., Pandey, D.N. & Bahuguna, D. Approximations of Solutions to a Fractional Differential Equation with a Deviating Argument. Differ Equ Dyn Syst 22, 333–352 (2014). https://doi.org/10.1007/s12591-013-0188-0

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