Properties of the solutions to periodic conformable non-autonomous non-instantaneous impulsive differential equations
DOI:
https://doi.org/10.58997/ejde.2024.30Abstract
In this article, we study properties of the solutions to periodic non-autonomous conformable non-instantaneous impulsive differential equations. We use a conformable Cauchy matrix and obtain some basic properties of the periodic solution to the homogeneous and non=homogeneous problems. We consider the periodicity of solutions to nonlinear problem via a fixed theorem.
For more information see https://ejde.math.txstate.edu/Volumes/2024/30/abstr.html
References
S. Abbas, M. Benchohra; Uniqueness and Ulam stabilities results for partial fractional differential equations with not instantaneous impulses, Applied Mathematics and Computation, 257 (2015), 190-198.
A. A. Abdelhakim, J. A. T. Machado; A critical analysis of the conformable derivative, Nonlinear Dynamics, 95 (2019), 3063-3073.
T. Abdeljawad; On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279 (2015), 57-66.
M. Abul-Ez, M. Zayed, A. Youssef, M. De la Sen; On conformable fractional Legendre polynomials and their convergence properties with applications, Alexandria Engineering Journal, 59 (2020), 5231-5245.
E. Alvarez, A. GLomez, M. Pinto; (Ö, c)-periodic functions and mild solutions to abstract fractional integro-differential equations, Electronic Journal of Qualitative Theory of Differential Equations, 2018 (2018) No. 16, 1-8.
M. Ayata, O. Ozkan; A new application of conformable Laplace decomposition method for fractional Newell-Whitehead-Segel equation, AIMS Mathematics, 5 (2020), 7402-7412.
L. Bai, J. J. Nieto; Variational approach to differential equations with not instantaneous impulses, Applied Mathematics Letters, 73 (2017), 44-48.
M. Bohner, V. F. Hatipo.glu; Dynamic cobweb models with conformable fractional derivatives, Nonlinear Analysis: Hybrid Systems, 32 (2019), 157-167.
P. Chen, Y. Li, H. Yang; Perturbation method for nonlocal impulsive evolution equations, Nonlinear Analysis-Hybrid Systems, 8 (2013), 22-30.
W. Chung; Fractional Newton mechanics with conformable fractional derivative, Journal of Computational and Applied Mathematics, 290 (2015), 150-158.
V. Colao, L. Muglia, H. Xu; An existence result for a new class of impulsive functional differential equations with delay, Journal of Mathematical Analysis and Applications, 441 (2016), 668-683.
E. HernLandez, D. OfRegan; On a new class of abstract impulsive differential equations, Porceedings of the American Mathematical Society, 141 (2013), 1641-1649.
M. Li, J.Wang, D. OfRegan; Existence and Ulamfs stability for conformable fractional differential equations with constant coefficients, Bulletin of the Malaysian Mathematical Sciences Society, 42 (2019), 1791-1812.
K. Liu, J. Wang, D. OfRegan, M. Fe.ckan; A new class of (Ö, c)-periodic non-instantaneous impulsive differential equations, Mediterranean Journal of Mathematics, 17 (2020), 155.
M. Pierri, H. R. HenrL.quez, A. Prokczyk; Global solutions for abstract differential equations with non-instantaneous impulses, Mediterranean Journal of Mathematics, 34 (2016), 1685- 1708.
M. Pierri, D. OfRegan, V. Rolnik; Existence of solutions for semi-linear abstract differential equations with not instantaneous impulses, Applied Mathematics and Computation, 219 (2013), 6743-6749.
A. G. Talafha, S. M. Alqaraleh, M. Al-Smadi, S. Hadid, S. Momani; Analytic solutions for a modified fractional three wave interaction equations with conformable derivative by unified method, Alexandria Engineering Journal, 59 (2020), 3731-3739.
Y. Tian, J. Wang, Y. Zhou; Almost periodic solutions for a class of non-instantaneous impulsive differential equations, Quaestiones Mathematicae, 42 (2019), 885-905.
F. Usta, M. Z. Sar.kaya; The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities, Demonstratio Mathematica, 52 (2019), 204-212.
J.Wang, A. G. Ibrahim, D. OfRegan, Y. Zhou; Controllability for noninstantaneous impulsive semilinear functional differential inclusions without compactness, Indagationes Mathematicae, 29 (2018), 1362-1392.
G. Xiao, J. Wang; Representation of solutions of linear conformable delay differential Equations, Applied Mathematics Letters, 117 (2021), 107088.
D. Yang, J. Wang; Non-instantaneous impulsive fractional-order implicit differential equations with random effects, Stochastic Analysis and Applications, 35 (2017), 719-741.
P. Yang, J. Wang, M. Fe.ckan; Boundedness, periodicity, and conditional stability of noninstantaneous impulsive evolution equations, Mathematical Methods in the Applied Sciences, 43 (2020), 5905-5926.
P. Yang, J. Wang, M. Fe.ckan; Periodic nonautonomous differential equations with noninstantaneous impulsive effects, Mathematical Methods in the Applied Sciences, 42 (2019), 3700-3720.
P. Yang, J. Wang, D. ORegan; Periodicity of non-homogeneous trajectories for noninstantaneous impulsive heat equations, Electronic Journal of Differential Equations, 2020 (2020) No. 18, 1-7.
Downloads
Published
License
Copyright (c) 2024 Yuanlin Ding, Kui Liu
This work is licensed under a Creative Commons Attribution 4.0 International License.
