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Results on neutral differential equation of sobolev type with nonlocal conditions

Author

Listed:
  • Kalimuthu, K.
  • Mohan, M.
  • Chokkalingam, R.
  • Nisar, Kottakkaran Sooppy

Abstract

In this work, we analyse the study of neutral fractional differential equation in an arbitrary Hilbert space. An associated integral equation is studied and approximate integral equation is obtained. We demonstrate the existence and uniqueness of an approximate solution by using analytic semigroup theory and the Fixed point method. In the application part, we discuss the approximation and the convergence results for such an approximation.

Suggested Citation

  • Kalimuthu, K. & Mohan, M. & Chokkalingam, R. & Nisar, Kottakkaran Sooppy, 2022. "Results on neutral differential equation of sobolev type with nonlocal conditions," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002703
    DOI: 10.1016/j.chaos.2022.112060
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    References listed on IDEAS

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    1. Fang Li & Gaston M. N'Guérékata, 2011. "An Existence Result for Neutral Delay Integrodifferential Equations with Fractional Order and Nonlocal Conditions," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-20, November.
    2. Kumar, Surendra & Sharma, Paras, 2022. "Faedo–Galerkin method for impulsive second-order stochastic integro-differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    3. Muslim, M., 2018. "Faedo–Galerkin approximation of second order nonlinear differential equation with deviated argument," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 315-324.
    4. Shruti Agarwal & Dhirendra Bahuguna, 2006. "Existence of solutions to Sobolev-type partial neutral differential equations," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-10, March.
    5. Kavitha, K. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy & Udhayakumar, R., 2021. "Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
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    Cited by:

    1. Veeresha, P., 2022. "The efficient fractional order based approach to analyze chemical reaction associated with pattern formation," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

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    More about this item

    Keywords

    Fractional differential equation; Analytic semigroup; Fixed point theorem; Nonlocal conditions; Faedo Galerkin approximation; Sobolev type;
    All these keywords.

    JEL classification:

    • K40 - Law and Economics - - Legal Procedure, the Legal System, and Illegal Behavior - - - General

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