On the existence and uniqueness of pseudo almost automorphic solutions for integro differential equations with reflection
- Authors
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- 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
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[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
- Issue
- Vol. 2 No. 1 (2024)
- Section
- Research Article
- License
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Copyright (c) 2024 Zahra Eidinejad

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