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Existence of solutions to Sobolev-type partial neutral differential equations

Author

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  • Shruti Agarwal
  • Dhirendra Bahuguna

Abstract

This work is concerned with a nonlocal partial neutral differential equation of Sobolev type. Specifically, existence of the solutions to the abstract formulations of such type of problems in a Banach space is established. The results are obtained by using Schauder's fixed point theorem. Finally, an example is provided to illustrate the applications of the abstract results.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnijsa:016308
    DOI: 10.1155/JAMSA/2006/16308
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    Cited by:

    1. Hamdy M. Ahmed & Mahmoud M. El-Borai & Hassan M. El-Owaidy & Ahmed S. Ghanem, 2019. "Existence Solution and Controllability of Sobolev Type Delay Nonlinear Fractional Integro-Differential System," Mathematics, MDPI, vol. 7(1), pages 1-14, January.
    2. 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).
    3. Hamdy M. Ahmed, 2017. "Sobolev-Type Fractional Stochastic Integrodifferential Equations with Nonlocal Conditions in Hilbert Space," Journal of Theoretical Probability, Springer, vol. 30(3), pages 771-783, September.

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