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Investigation on the Approximate Controllability of Fractional Differential Systems with State Delay

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Abstract

In this article, we presented some sufficient conditions for the approximate controllability of a class of fractional differential systems with fixed delay in Banach space. The existence of a mild solution is discussed with the help of the fixed point theorem. Controllability results are obtained using generalized Gronwall’s inequality, Cauchy sequence, and the basics of functional analysis. As a last note, we have included an example for the illustration of the obtained theory.

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Authors and Affiliations

  1. Department of Mathematics, Bherulal Patidar Govt P.G. College MHOW, Indore, 453441, India

    Ajay Kumar

  2. Department of Mathematics, Government PG College Bisalpur, Pilibhit, 262201, India

    Rohit Patel

  3. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamilnadu, 632 014, India

    Velusamy Vijayakumar

  4. Department of Applied Sciences, Rajkiya Engineering College Kannauj, Kannauj, 209732, India

    Anurag Shukla

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  1. Ajay Kumar
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  2. Rohit Patel
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  3. Velusamy Vijayakumar
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  4. Anurag Shukla
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Correspondence to Anurag Shukla.

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Kumar, A., Patel, R., Vijayakumar, V. et al. Investigation on the Approximate Controllability of Fractional Differential Systems with State Delay. Circuits Syst Signal Process 42, 4585–4602 (2023). https://doi.org/10.1007/s00034-023-02335-0

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