Novel Insights into Oscillation of Impulsive Fractional Differential Equations with Caputo Derivative
DOI:
https://doi.org/10.71107/977nnr55Keywords:
Oscillation theory, fractional differential equation, impulsive differential equationsAbstract
In this paper, we explore the oscillation of impulsive Caputo fractional differential equations. Conditions for both asymptotic and oscillatory outcomes are established through the application of the inequality principle and Bihari Lemma. An example is given to explain the results of all problems. This is the first time to study the oscillation of impulsive fractional differential equation with Caputo Derivative.
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[1] A. Hermosillo-Arteaga, M. P. Romo, and M. T. Roberto, “Response spectra generation using a fractional differential model,” Soil Dynamics and Earthquake Engineering 115, 719– 729 (2018).
[2] Y. Jiang, B. Xia, X. Zhao, et al., “Data-based fractional differential models for non-linear dynamic modeling of a lithium-ion battery,” Energy 135, 171–181 (2017).
[3] A. Ortega, J. J. Rosales, J. M. Cruz-Duarte, et al., “Fractional model of the dielectric dispersion,” Optik-International Journal for Light and Electron Optics 180, 754–759 (2019).
[4] L. Feng and S. Sun, “Oscillation theorems for three class of conformable fractional differential equations,” Advances in Difference Equations 2019, 1–30 (2019).
[5] Y. Wang, Z. Han, and S. Sun, “Comment on “on the oscillation of fractional–order delay differential equations with constant coefficients”,” Communications in Nonlinear Science and Numerical Simulation 26, 195–200 (2015).
[6] Y. Wang, Z. Han, P. Zhao, et al., “Oscillation theorems for fractional neutral differential equations,” Hacettepe Journal of Mathematics and Statistics 44, 1477–1488 (2015).
[7] L. Xu, J. Li, and S. Ge, “Impulsive stabilization of fractional differential systems,” ISA Transactions 70, 12–131 (2017).
[8] Y. Zhou, B. Ahmad, and A. Alsaedi, “Existence of non oscillatory solutions for fractional neutral differential equations,” Applied Mathematics Letters 72, 70–74 (2017).
[9] Y. Zhou, B. Ahmad, F. Chen, et al., “Oscillation for fractional partial differential equations,” Bulletin of the Malaysian Mathematical Sciences Society 42, 449–465 (2019).
[10] Y. Zhou, B. Ahmad, and A. Alsaedi, “Existence of non oscillatory solutions for fractional functional differential equations,” Bulletin of the Malaysian Mathematical Sciences Society 42, 751–766 (2019).
[11] T. Guo, “Controllability and observability of impulsive fractional linear time-invariant system,” Computers and Mathematics with Applications 64, 3171–3182 (2012).
[12] I. Stamova, “Global stability of impulsive fractional differential equations,” Applied Mathematics and Computation 237, 605–612 (2014).
[13] J. Wang, X. Li, and W. Wei, “On the natural solution of an impulsive fractional differential equation of order q ∈ (1 , 2),” Communications in Nonlinear Science and Numerical Simulation 17, 4384–4394 (2012).
[14] S. R. Grace, R. P. Agarwal, J. Y. Wong, and A. Zafer, “On the oscillation of fractional differential equations,” Fractional Calculus and Applied Analysis 15, 222–231 (2012).
[15] A. Raheem and M. Maqbul, “Oscillation criteria for impulsive partial fractional differential equations,” Computers and Mathematics with Applications 73, 1781 1788 (2017).
[16] I. Bihari, “Researches of the boundedness and stability of the solutions of non-linear differential equations,” Acta Mathematica Hungarica 8, 261–278 (1957).
[17] M. Benchohra, S. Hamani, and Y. Zhou, “Oscillation and nonoscillation for caputo-hadamard impulsive fractional differential inclusions,” Advances in Difference Equations 2019, 1–15 (2019).
[18] S. R. Grace, “On the oscillatory behaviour of solutions of nonlinear fractional differential equations,” Applied Mathematics and Computation 266, 259–266 (2015).
[19] Q. Ma, J. Pecaric, and J. Zhang, “Integral inequalities of systems and the estimate for solutions of certain nonlinear twodimensional fractional differential systems,” Computers and Mathematics with Applications 61, 3258–3267 (2011).
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Data will be made available on request from corresponding author.
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Copyright (c) 2025 Rabbiya Fatima, Azmat Ullah Khan Niazi, Hassan Raza (Author)

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