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New existence results on nonlocal neutral fractional differential equation in concepts of Caputo derivative with impulsive conditions

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  • Kaliraj, K.
  • Manjula, M.
  • Ravichandran, C.

Abstract

In this article, we examine a nonlinear impulsive neutral fractional differential equation with nonlocal condition in an arbitrary Hilbert space. We obtain an associated integral equation and then consider a sequence of approximate integral equations by the projection of considered associated nonlocal neutral fractional integral equation onto finite dimensional space. The existence and uniqueness of an approximate solution by using analytic semigroup theory and the Fixed-point method are demonstrated. Convergence of the solutions of the approximate integral equation is proved. The Faedo-Galerkin approximation of the solution is studied and demonstrated some convergence results. Lastly, the application is presented to illustrate the theory of the main results.

Suggested Citation

  • Kaliraj, K. & Manjula, M. & Ravichandran, C., 2022. "New existence results on nonlocal neutral fractional differential equation in concepts of Caputo derivative with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922004945
    DOI: 10.1016/j.chaos.2022.112284
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    1. Pallavi Bedi & Aziz Khan & Anoop Kumar & Thabet Abdeljawad, 2022. "Computational Study Of Fractional-Order Vector Borne Diseases Model," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-12, August.
    2. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Atangana, Abdon, 2018. "Blind in a commutative world: Simple illustrations with functions and chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 347-363.
    4. Nisar, Kottakkaran Sooppy & Jothimani, K. & Kaliraj, K. & Ravichandran, C., 2021. "An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
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    Cited by:

    1. Lakshmi Priya, P.K. & Kaliraj, K., 2022. "An application of fixed point technique of Rothe’s-type to interpret the controllability criteria of neutral nonlinear fractional ordered impulsive system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Zhiyuan Yuan & Luyao Wang & Wenchang He & Ning Cai & Jia Mu, 2024. "Fractional Neutral Integro-Differential Equations with Nonlocal Initial Conditions," Mathematics, MDPI, vol. 12(12), pages 1-14, June.
    3. Nisar, Kottakkaran Sooppy & Logeswari, K. & Ravichandran, C. & Sabarinathan, S., 2023. "New frame of fractional neutral ABC-derivative with IBC and mixed delay," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).

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