Existence and asymptotic stability of continuous solutions for a general form of integral equations of product type

Article Sidebar

pdf
Published: Jul 1, 2023
DOI: https://doi.org/10.58205/jiamcs.v3i1.204
Keywords:
d point theorem. Keywords: Neutral integral equations of product type, Darbo’s fixed point theorem, Continuous solution, Asymptotic stable solution.

Main Article Content

Azzeddine Bellour
Ecole Normale Supérieure de Constantine
https://orcid.org/0000-0002-3644-0804
Mahmoud Bousselsal
Ecole Normale Supérieure de Kouba, Algeria,École Normale Supérieure de Kouba

Abstract

In this work, we study the existence and the asymptotic stability of the continuous solutions for a general form for neutral integral equations of product type. Our result will given in more general and easy conditions; Moreover, the neutral integral equation of product type given in this work contains many particular forms which are studied recently. The analysis uses the techniques of measures of non-compactness and Darbo’s fixed point theorem.


 


 

Downloads

Download data is not yet available.

Article Details

How to Cite
[1]
Bellour, A. and Bousselsal, M. 2023. Existence and asymptotic stability of continuous solutions for a general form of integral equations of product type. Journal of Innovative Applied Mathematics and Computational Sciences. 3, 1 (Jul. 2023), 66–74. DOI:https://doi.org/10.58205/jiamcs.v3i1.204.
Issue
Vol. 3 No. 1 (2023): January-June
Section
Research Articles
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

  • Authors keep the rights and guarantee the Journal of Innovative Applied Mathematics and Computational Sciences  the right to be the first publication of the document, licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License that allows others to share the work with an acknowledgement of authorship and publication in the journal.
  • Authors are allowed and encouraged to spread their work through electronic means using personal or institutional websites (institutional open archives, personal websites or professional and academic networks profiles) once the text has been published.
Author Biography

Mahmoud Bousselsal, Ecole Normale Supérieure de Kouba, Algeria,École Normale Supérieure de Kouba

integral equations

 

Crossref
Scopus
Google Scholar
Europe PMC

References

Bailey, N. (1975). The Mathematical Theory of Infectious Diseases and Its Applications. New York: Hafner.

Ardjouni, A., & Djoudi, A. (2019). Approximating solutions of nonlinear hybrid Caputo fractional integro-differential equations via Dhage iteration principle. Ural Mathematical Journal, 5, 3-12.

Abdeldaim, A. (2012). On some new Gronwall-Bellman-Ou-Iang type integral inequalities to study certain epidemic models. Journal of Integral Equations and Applications, 24, 149-166.

Banas, J., & Goebel, K. (1980). Measures of Noncompactness in Banach Spaces, in: Lecture Notes in Pure and Applied Mathematics (م 60). New York: Dekker.

Banas, J., & Rzepka, B. (2003). On existence and asymptotic stability of solutions of a nonlinear integral equation. Journal of Mathematical Analysis and Applications, 284, 165-173.

Banas, J., & Rivero, J. (1988). On measures of weak noncompactness. Annali Di Matematica Pura Ed Applicata, 151, 213-224.

Banas, J., & Olszowy, L. (2001). Measures of noncompactness related to monotonicity. Commentationes Mathematicae, 41, 13-23.

Bellour, A., Bousselsal, M., & Taoudi, M. (2014). Integrable solutions of a nonlinear integral equation related to some epidemic models. Glasnik Matematicki, 49, 395-406.

Boulfoul, B., Bellour, A., & Djebali, S. (2018). Solvability of nonlinear integral equations of product type. Electronic Journal of Differential Equations, 19, 1-20.

Gripenberg, G. (1981). On some epidemic models. Quarterly of Applied Mathematics, 39, 317-327.

Gripenberg, J. (1980). Periodic solutions of an epidemic model. Journal of Mathematical Biology, 10, 271-280.

Bousselsal, M., & Bellour, A. (2021). Existence and asymptotic stability of continuous solutions for integral equations of product type. Journal of Innovative Applied Mathematics and Computational Sciences, 1(1), 1-9.

Diekmann, O. (1979). Run for your life, A note on the asymptotic speed of propagation of an epidemic+. Journal of Differential Equations, 33, 58-73.

Li, L., Meng, F., & Ju, P. (2011). Some new integral inequalities and their applications in studying the stability of nonlinear integro-differential equations with time delay. Journal of Mathematical Analysis and Applications, 377, 853-862.

Olaru, I. (2010). Generalization of an integral equation related to some epidemic models. Carpathian Journal of Mathematics, 26, 92-96.

METWALI, M., & MISHRA, V. (2023). On the measure of noncompactness in Lp(R+)

and applications to a product of n

-integral equations. Turkish Journal of Mathematics, 47, 372-386.

Pachpatte, B. (1995). On a new inequality suggested by the study of certain epidemic models. Journal of Mathematical Analysis and Applications, 195, 638-644.

Waltman, P. (1974). Deterministic Threshold Models in the Theory of Epidemics, Lecture Notes in Biomathematics (م 1). New York: Springer-Verlag.