10.25673/122863">


Proceedings of International Conference on Applied Innovation in IT
2025/12/22, Volume 13, Issue 5, pp.291-296

Existence and Stability Analysis of Nonlinear Volterra-Fredholm Integral Equations


Shahab A. Hassan, Noor H. Abdullah and Waleed A. Saeed


Abstract: The aim of this paper is to prove the existence and uniqueness of a solution for a Volterra-Fredholm nonlinear integral equation in two variables under certain conditions, for example, Using the Lipschitz condition with Banach's space contraction principle, under assumptions (i)-(iv), a unique solution exists in Banach's space Z. Moreover, we examine some fundamental characteristics of the solutions for a Volterra-Fredholm nonlinear integral equation in two variables which occur in applications using the inequality established in [6, Theorem 1]. It has also been demonstrated that the functions and parameters included in the equation under investigation continuously influence the behavior of solutions under perturbations in parameters. This investigation may allow for the extension of findings. and the last section contains an illustrative example for the validity of the obtained results. making the method much more attractive for practical applications. The examples show the method is straightforward and effective, and the method can also be extended to other nonlinear integral equation problems.

Keywords: Integral equation , Volterra-Fredholm , Existence and uniqueness of solution , Properties of solutions, Banach fixed-point.

DOI: 10.25673/122863

Download: PDF

References:

  1. B. L. Moiseiwitsch, Integral Equations. London, UK: Longman, 1977.
  2. B. G. Pachpatte, “On mixed Volterra-Fredholm type integral equations,” Indian J. Pure Appl. Math., vol. 17, no. 4, pp. 488-496, 1986.
  3. H. R. Thieme, “A model for the spatial spread of an epidemic,” J. Math. Biol., vol. 4, no. 4, pp. 337-351, 1977, [Online]. Available: https://doi.org/10.1007/BF00275030.
  4. O. Diekmann, “Thresholds and traveling waves for the geographical spread of infection,” J. Math. Biol., vol. 6, no. 2, pp. 109-130, 1978, [Online]. Available: https://doi.org/10.1007/BF00277864.
  5. C. Corduneanu, “Abstract Volterra equations: a survey,” Math. Comput. Model., vol. 32, no. 11-13, pp. 1503-1528, 2000, [Online]. Available: https://doi.org/10.1016/S0895-7177(00)00216-9.
  6. A. M. Wazwaz, Linear and Nonlinear Integral Equations: Methods and Applications. Beijing, China: Higher Education Press and Berlin: Springer, 2011, [Online]. Available: https://doi.org/10.1007/978-3-642-21449-3.
  7. B. G. Pachpatte, “On Volterra-Fredholm integral equation in two variables,” Demonstratio Math., vol. 40, no. 4, pp. 839-852, 2007, [Online]. Available: https://doi.org/10.1515/dema-2007-0410.
  8. B. G. Pachpatte, “New bounds on certain fundamental integral inequalities,” J. Math. Inequal., vol. 4, no. 3, pp. 405-412, 2010, [Online]. Available: https://doi.org/10.7153/jmi-04-37.
  9. B. G. Pachpatte, “Inequalities applicable to mixed Volterra-Fredholm type integral equations,” An. Sti. Univ. Al. I. Cuza Iasi Math., vol. 56, no. 1, pp. 17-24, 2010.
  10. B. G. Pachpatte, Inequalities for Differential and Integral Equations. San Diego, CA, USA: Academic Press, 1998, [Online]. Available: https://doi.org/10.1016/S0076-5392(98)X8001-X.
  11. B. G. Pachpatte, “Growth estimates on mixed Volterra-Fredholm type integral inequalities,” Fasc. Math., vol. 42, pp. 63-72, 2009.
  12. B. G. Pachpatte, “On a general mixed Volterra-Fredholm integral equation,” An. Sti. Univ. Al. I. Cuza Iasi Math., vol. 56, pp. 17-24, 2010, [Online]. Available: https://doi.org/10.2478/v10157-010-0002-z.
  13. B. G. Pachpatte, Multidimensional Integral Equations and Inequalities. Amsterdam, Netherlands: Elsevier (Springer), 2011, [Online]. Available: https://doi.org/10.1016/S0076-5392(11)X0001-3.
  14. C. Bacotiu, “On mixed nonlinear integral equations of Volterra-Fredholm type with modified argument,” Studia Univ. Babes-Bolyai, Math., vol. 54, no. 1, pp. 29-41, 2009.
  15. H. Vu and L. S. Dong, “Existence and Uniqueness of Solution for Two-Dimensional Fuzzy Volterra-Fredholm Integral Equation,” Thai J. Math., vol. 19, no. 4, pp. 1355-1365, 2021.

    HOME

       - Conference
       - Journal
       - Paper Submission to Conference
       - Paper Submission to Journal
       - Fee Payment
       - For Authors
       - For Reviewers
       - Important Dates
       - Conference Committee
       - Editorial Board
       - Reviewers
       - Last Proceeding


    PROCEEDINGS

       - Volume 13, Issue 5 (ICAIIT 2025)
       - Volume 13, Issue 4 (ICAIIT 2025)
       - Volume 13, Issue 3 (ICAIIT 2025)
       - Volume 13, Issue 2 (ICAIIT 2025)
       - Volume 13, Issue 1 (ICAIIT 2025)
       - Volume 12, Issue 2 (ICAIIT 2024)
       - Volume 12, Issue 1 (ICAIIT 2024)
       - Volume 11, Issue 2 (ICAIIT 2023)
       - Volume 11, Issue 1 (ICAIIT 2023)
       - Volume 10, Issue 1 (ICAIIT 2022)
       - Volume 9, Issue 1 (ICAIIT 2021)
       - Volume 8, Issue 1 (ICAIIT 2020)
       - Volume 7, Issue 1 (ICAIIT 2019)
       - Volume 7, Issue 2 (ICAIIT 2019)
       - Volume 6, Issue 1 (ICAIIT 2018)
       - Volume 5, Issue 1 (ICAIIT 2017)
       - Volume 4, Issue 1 (ICAIIT 2016)
       - Volume 3, Issue 1 (ICAIIT 2015)
       - Volume 2, Issue 1 (ICAIIT 2014)
       - Volume 1, Issue 1 (ICAIIT 2013)


    LAST CONFERENCE

       ICAIIT 2026
         - Photos
         - Reports

    PAST CONFERENCES

    ETHICS IN PUBLICATIONS

    ACCOMODATION

    CONTACT US

 

        

         Proceedings of the International Conference on Applied Innovations in IT by Anhalt University of Applied Sciences is licensed under CC BY-SA 4.0


                                                   This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License


           ISSN 2199-8876
           Publisher: Edition Hochschule Anhalt
           Location: Anhalt University of Applied Sciences
           Email: leiterin.hsb@hs-anhalt.de
           Phone: +49 (0) 3496 67 5611
           Address: Building 01 - Red Building, Top floor, Room 425, Bernburger Str. 55, D-06366 Köthen, Germany

        site traffic counter

Creative Commons License
Except where otherwise noted, all works and proceedings on this site is licensed under Creative Commons Attribution-ShareAlike 4.0 International License.