On the existence and uniqueness of pseudo almost automorphic solutions for integro differential equations with reflection

Authors
  • Zahra Eidinejad

    School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran

Keywords:
integro differential equation, reflection, Mittag-Leffler function
Abstract
In this paper we apply fixed point theory and measure theory to investigate the existence of unique solutions for  integro differential equations with reflection (IDE-R). Using almost automorphic functions, we study the solutions of these equations, which are of pseudo almost automorphic \(($\mathscr{PAA}$)\) type, by introducing the Mittag-Lefler function. Finally, we present an example we illustrate the application of the main results obtained.
References

[1] El Hadi Ait Dads, Khalil E, and M. Miraoui, (µ, ν)-pseudo almost automorphic solutions for some non-autonomous differential equations, International Journal of Mathematics 26 (2015), no. 11, Article 1550090, 21 pages.

[2] J. Blot, Ph. Cieutat, and Kh. Ezzinbi, Measure theory and pseudo almost automorphic functions: new developments and applications, Nonlinear Analysis 75 (2012), no. 4, 2426–2447.

[3] S. Bochner, Continuous mappings of almost automorphic and almost periodic functions, Proceedings of the National Academy of Sciences of the United States of America 52 (1964), 907–910.

[4] Elhadi A. Dads, S. Fatajou, and L. Khachimi, Pseudo almost automorphic solutions for differential equations involving reflection of the argument, ISRN Mathematical Analysis (2012), Article ID 626490, 20 pages.

[5] T. Diagana, Pseudo almost periodic solutions to some differential equations, Nonlinear Analysis 60 (2005), no. 7, 1277–1286.

[6] T. Diagana, Kh. Ezzinbi, and M. Miraoui, Pseudo-almost periodic and pseudo-almost automorphic solutions to some evolution equations involving theoretical measure theory, Cubo 16 (2014), no. 2, 1–31, MR3237503.

[7] Z. Eidinejad, R. Saadati, and R. Mesiar, Optimum Approximation for ς-Lie Homomorphisms and Jordan ς-Lie Homomorphisms in ς-Lie Algebras by Aggregation Control Functions, Mathematics 10 (2022), no. 10, 1704, Article 1704.

[8] Ch. P. Gupta, Existence and uniqueness theorems for boundary value problems involving reflection of the argument, Nonlinear Analysis 11 (1987), no. 9, 1075–1083.

[9] Ch. P. Gupta, Two-point boundary value problems involving reflection of the argument, International Journal of Mathematics and Mathematical Sciences 10 (1987), no. 2, 361–371.

[10] F. Kong and J. J. Nieto, Almost periodic dynamical behaviors of the hematopoiesis model with mixed discontinuous harvesting terms, Discrete and Continuous Dynamical Systems – Series B 24 (2019), no. 11, 5803–5830.

[11] M. Miraoui and D. D. Repovš, Existence results for integro-differential equations with reflection, Numerical Functional Analysis and Optimization 42 (2021), no. 8, 919–934, MR4284921.

[12] Gaston M. N’Guerekata, Almost Automorphic and Almost Periodic Functions in Abstract Spaces, Kluwer Academic/Plenum Publishers, New York, 2001.

[13] Nikolaos S. Papageorgiou, Vicentiu D. Rădulescu, and Dušan D. Repovš, Periodic solutions for a class of evolution inclusions, Computers & Mathematics with Applications 75 (2018), no. 8, 3047–3065.

[14] N. Xin and D. Piao, Weighted pseudo almost periodic solutions for differential equations involving reflection of the argument, International Journal of Physical Sciences 7 (2012), no. 11, 1806–1810.

Additional Files
Published
18-11-2024
Section
Research Article
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Copyright (c) 2024 Zahra Eidinejad

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

How to Cite

On the existence and uniqueness of pseudo almost automorphic solutions for integro differential equations with reflection. (2024). Letters on Applied and Pure Mathematics, 2(1), 53-62. https://doi.org/10.66147/lapm.20253133

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