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Journal articles on the topic 'Impulsive fractional differential equations'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Fečkan, Michal, and Jin Rong Wang. "Periodic impulsive fractional differential equations." Advances in Nonlinear Analysis 8, no. 1 (2017): 482–96. http://dx.doi.org/10.1515/anona-2017-0015.

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Abstract This paper deals with the existence of periodic solutions of fractional differential equations with periodic impulses. The first part of the paper is devoted to the uniqueness, existence and asymptotic stability results for periodic solutions of impulsive fractional differential equations with varying lower limits for standard nonlinear cases as well as for cases of weak nonlinearities, equidistant and periodically shifted impulses. We also apply our result to an impulsive fractional Lorenz system. The second part extends the study to periodic impulsive fractional differential equatio

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2

Sadhasivam, V., and M. Deepa. "Oscillation criteria for fractional impulsive hybrid partial differential equations." Issues of Analysis 26, no. 2 (2019): 73–91. http://dx.doi.org/10.15393/j3.art.2019.5910.

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3

Fečkan, Michal, Marius-F. Danca, and Guanrong Chen. "Fractional Differential Equations with Impulsive Effects." Fractal and Fractional 8, no. 9 (2024): 500. http://dx.doi.org/10.3390/fractalfract8090500.

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This paper discusses impulsive effects on fractional differential equations. Two approaches are taken to obtain our results: either with fixed or changing lower limits in Caputo fractional derivatives. First, we derive an existence result for periodic solutions of fractional differential equations with periodically changing lower limits. Then, the impulsive effects are modeled for fractional differential equations regarding the nonlinearities rather than the initial value conditions. The proposed impulsive model differs from common discontinuous and nonsmooth dynamical systems.

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4

Guo, Tian Liang, and Wei Jiang. "Impulsive fractional functional differential equations." Computers & Mathematics with Applications 64, no. 10 (2012): 3414–24. http://dx.doi.org/10.1016/j.camwa.2011.12.054.

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5

Guo, Tian Liang, and KanJian Zhang. "Impulsive fractional partial differential equations." Applied Mathematics and Computation 257 (April 2015): 581–90. http://dx.doi.org/10.1016/j.amc.2014.05.101.

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6

Stamov, Gani, Anatoliy Martynyuk, and Ivanka Stamova. "Impulsive Fractional-Like Differential Equations: Practical Stability and Boundedness with Respect to h-Manifolds." Fractal and Fractional 3, no. 4 (2019): 50. http://dx.doi.org/10.3390/fractalfract3040050.

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In this paper, an impulsive fractional-like system of differential equations is introduced. The notions of practical stability and boundedness with respect to h-manifolds for fractional-like differential equations are generalized to the impulsive case. For the first time in the literature, Lyapunov-like functions and their derivatives with respect to impulsive fractional-like systems are defined. As an application, an impulsive fractional-like system of Lotka–Volterra equations is considered and new criteria for practical exponential stability are proposed. In addition, the uncertain case is a

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7

A A Abuharbid, Suzan, Kholoud W Saleem, and Salima Kh Ahmed. "The Oscillations for Delay Impulsive Fractional Partial Differential Equations (IFPDEs)." International Journal of Science and Research (IJSR) 11, no. 1 (2022): 1366–71. http://dx.doi.org/10.21275/mr22125031520.

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8

Mahto, Lakshman, Syed Abbas, and Angelo Favini. "Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications." International Journal of Differential Equations 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/704547.

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We use Sadovskii's fixed point method to investigate the existence and uniqueness of solutions of Caputo impulsive fractional differential equations of order with one example of impulsive logistic model and few other examples as well. We also discuss Caputo impulsive fractional differential equations with finite delay. The results proven are new and compliment the existing one.

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9

Ma, Changyou. "A Novel Computational Technique for Impulsive Fractional Differential Equations." Symmetry 11, no. 2 (2019): 216. http://dx.doi.org/10.3390/sym11020216.

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A computational technique for impulsive fractional differential equations is proposed in this paper. Adomian decomposition method plays an efficient role for approximate analytical solutions for ordinary or fractional calculus. Semi-analytical method is proposed by use of the Adomian polynomials. The method successively updates the initial values and gives the numerical solutions on different impulsive intervals. As one of the numerical examples, an impulsive fractional logistic differential equation is given to illustrate the method.

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10

Ahmed, Hamdy, A. Hassan, and A. Ghanem. "Nonlinear Impulsive Fractional Integro Differential Equations." British Journal of Mathematics & Computer Science 10, no. 4 (2015): 1–11. http://dx.doi.org/10.9734/bjmcs/2015/18725.

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11

Yukunthorn, Weera, Sotiris K. Ntouyas, and Jessada Tariboon. "Impulsive Multiorders Riemann-Liouville Fractional Differential Equations." Discrete Dynamics in Nature and Society 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/603893.

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Impulsive multiorders fractional differential equations are studied. Existence and uniqueness results are obtained for first- and second-order impulsive initial value problems by using Banach’s fixed point theorem in an appropriate weighted space. Examples illustrating the main results are presented.

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12

Wu, Guo–Cheng, De–Qiang Zeng, and Dumitru Baleanu. "Fractional impulsive differential equations: Exact solutions, integral equations and short memory case." Fractional Calculus and Applied Analysis 22, no. 1 (2019): 180–92. http://dx.doi.org/10.1515/fca-2019-0012.

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Abstract Fractional impulsive differential equations are revisited first. Some fundamental solutions of linear cases are given in this study. One straightforward technique without using integral equation is adopted to obtain exact solutions which are given by use of piecewise functions. Furthermore, a class of short memory fractional differential equations is proposed and the variable case is discussed. Mittag–Leffler solutions with impulses are derived which both satisfy the equations and impulsive conditions, respectively.

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13

Moumen, Abdelkader, Mohamed Ferhat, Amin Benaissa Cherif, Mohamed Bouye, and Mohamad Biomy. "A System of Coupled Impulsive Neutral Functional Differential Equations: New Existence Results Driven by Fractional Brownian Motion and the Wiener Process." Mathematics 11, no. 24 (2023): 4949. http://dx.doi.org/10.3390/math11244949.

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Conditions for the existence and uniqueness of mild solutions for a system of semilinear impulsive differential equations with infinite fractional Brownian movements and the Wiener process are established. Our approach is based on a novel application of Burton and Kirk’s fixed point theorem in extended Banach spaces. This paper aims to extend current results to a differential-inclusions scenario. The motivation of this paper for impulsive neutral differential equations is to investigate the existence of solutions for impulsive neutral differential equations with fractional Brownian motion and

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14

Liu, Yuji. "A new method for converting boundary value problems for impulsive fractional differential equations to integral equations and its applications." Advances in Nonlinear Analysis 8, no. 1 (2017): 386–454. http://dx.doi.org/10.1515/anona-2016-0064.

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Abstract In this paper, we present a new method for converting boundary value problems of impulsive fractional differential equations to integral equations. Applications of this method are given to solve some types of anti-periodic boundary value problems for impulsive fractional differential equations. Firstly by using iterative method, we prove existence and uniqueness of solutions of Cauchy problems of differential equations involving Caputo fractional derivative, Riemann–Liouville and Hadamard fractional derivatives with order {q\in(0,1)} , see Theorem 2, Theorem 4, Theorem 6 and Theorem 8

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15

Chu, Limin, Weimin Hu, Youhui Su, and Yongzhen Yun. "Existence and Uniqueness of Solutions to Four-Point Impulsive Fractional Differential Equations with p-Laplacian Operator." Mathematics 10, no. 11 (2022): 1852. http://dx.doi.org/10.3390/math10111852.

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In this paper, by using fixed-point theorems, the existence and uniqueness of positive solutions to a class of four-point impulsive fractional differential equations with p-Laplacian operators are studied. In addition, three examples are given to justify the conclusion. The interest of this paper is to study impulsive fractional differential equations with p-Laplacian operators.

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16

Chen, Xingru, Haibo Gu, and Yu Sun. "Optimal Controls for a Class of Impulsive Katugampola Fractional Differential Equations with Nonlocal Conditions." Journal of Function Spaces 2020 (December 1, 2020): 1–9. http://dx.doi.org/10.1155/2020/3142801.

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In this paper, we investigate a class of impulsive Katugampola fractional differential equations with nonlocal conditions in a Banach space. First, by using a fixed-point theorem, we obtain the existence results for a class of impulsive Katugampola fractional differential equations. Secondly, we derive the sufficient conditions for optimal controls by building approximating minimizing sequences of functions twice.

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17

Xie, Tingting, and Mengmeng Li. "Finite-Time Stability of Impulsive Fractional Differential Equations with Pure Delays." Axioms 12, no. 12 (2023): 1129. http://dx.doi.org/10.3390/axioms12121129.

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This paper introduces a novel concept of the impulsive delayed Mittag–Leffler-type vector function, an extension of the Mittag–Leffler matrix function. It is essential to seek explicit formulas for the solutions to linear impulsive fractional differential delay equations. Based on explicit formulas of the solutions, the finite-time stability results of impulsive fractional differential delay equations are presented. Finally, we present four examples to illustrate the validity of our theoretical results.

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18

Hannabou, Mohamed, and Hilal Khalid. "Investigation of a Mild Solution to Coupled Systems of Impulsive Hybrid Fractional Differential Equations." International Journal of Differential Equations 2019 (December 10, 2019): 1–9. http://dx.doi.org/10.1155/2019/2618982.

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The study of coupled systems of hybrid fractional differential equations requires the attention of scientists for the exploration of their different important aspects. Our aim in this paper is to study the existence and uniqueness of the solution for impulsive hybrid fractional differential equations. The novelty of this work is the study of a coupled system of impulsive hybrid fractional differential equations with initial and boundary hybrid conditions. We used the classical fixed-point theorems such as the Banach fixed-point theorem and Leray–Schauder alternative fixed-point theorem for exi

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19

Metpattarahiran, Chanisara, Kulandhaivel Karthikeyan, Panjaiyan Karthikeyann, and Thanin Sitthiwirattham. "On Hilfer-Type Fractional Impulsive Differential Equations." International Journal of Differential Equations 2022 (June 14, 2022): 1–12. http://dx.doi.org/10.1155/2022/7803065.

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Using the Schauder fixed point theorem, we prove the existence of impulsive fractional differential equations using Hilfer fractional derivative and nearly sectorial operators in this paper. We’ve gone over the two scenarios where the related semigroup is compact and noncompact for this purpose. We also go over an example to back up the main points.

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20

Agarwal, Ravi P., Snezhana Hristova, and Donal O’Regan. "The Strict Stability of Impulsive Differential Equations with a Caputo Fractional Derivative with Respect to Other Functions." Fractal and Fractional 9, no. 6 (2025): 341. https://doi.org/10.3390/fractalfract9060341.

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The aim of this paper is to study a nonlinear system of impulsive fractional differential equations and Caputo fractional derivatives with respect to another function (CFF). The main characteristics of these fractional derivatives are two-fold: first, the lower limit of CFF equals the impulsive time of the considered interval; second, the applied function in CFF is changeable at each interval without impulses. An auxiliary system of two linear scalar impulsive fractional differential equations with CFF is considered, and strict stability in a couple is defined. The behavior of its solutions is

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21

Liu, Xianghu, and Yanfang Li. "Some Antiperiodic Boundary Value Problem for Nonlinear Fractional Impulsive Differential Equations." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/571536.

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This paper is concerned with the sufficient conditions for the existence of solutions for a class of generalized antiperiodic boundary value problem for nonlinear fractional impulsive differential equations involving the Riemann-Liouville fractional derivative. Firstly, we introduce the fractional calculus and give the generalized R-L fractional integral formula of R-L fractional derivative involving impulsive. Secondly, the sufficient condition for the existence and uniqueness of solutions is presented. Finally, we give some examples to illustrate our main results.

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22

Kucche, Kishor D., Jyoti P. Kharade та J. Vanterler da C. Sousa. "ON THE NONLINEAR IMPULSIVE Ψ–HILFER FRACTIONAL DIFFERENTIAL EQUATIONS". Mathematical Modelling and Analysis 25, № 4 (2020): 642–60. http://dx.doi.org/10.3846/mma.2020.11445.

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In this paper, we consider the nonlinear Ψ-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of solutions. The acquired results are extended to the nonlocal Ψ-Hilfer impulsive fractional differential equation. We gave an applications to the outcomes we obtained. Further, examples are provided in support of the results we got.

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23

Benchohra, Mouffak, and Djamila Seba. "Impulsive fractional differential equations in Banach spaces." Electronic Journal of Qualitative Theory of Differential Equations, no. 8 (2009): 1–14. http://dx.doi.org/10.14232/ejqtde.2009.4.8.

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24

Benchohra, Mouffak, and Farida Berhoun. "Impulsive fractional differential equations with variable times." Computers & Mathematics with Applications 59, no. 3 (2010): 1245–52. http://dx.doi.org/10.1016/j.camwa.2009.05.016.

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25

Tariboon, Jessada, and Sotiris K. Ntouyas. "Oscillation of impulsive conformable fractional differential equations." Open Mathematics 14, no. 1 (2016): 497–508. http://dx.doi.org/10.1515/math-2016-0044.

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AbstractIn this paper, we investigate oscillation results for the solutions of impulsive conformable fractional differential equations of the form$$\left\{ \begin{array}{l} {t_k}{D^\alpha }\left( {p\left( t \right)\left[ {{t_k}{D^\alpha }x\left( t \right) + r\left( t \right)x\left( t \right)} \right]} \right) + q\left( t \right)x\left( t \right) = 0,\quad t \ge {t_0},\;t \ne {t_k},\\ x\left( {t_k^ + } \right) = {a_k}x(t_k^ - ),\quad {t_k}{D^\alpha }x\left( {t_k^ + } \right) = {b_{k\;{t_{k - 1}}}}{D^\alpha }x(t_k^ - ),\quad \;k = 1,2, \ldots. \end{array} \right.$$Some new oscillation results ar

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26

Stamova, Ivanka. "Global stability of impulsive fractional differential equations." Applied Mathematics and Computation 237 (June 2014): 605–12. http://dx.doi.org/10.1016/j.amc.2014.03.067.

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27

Xu, Liguang, Hongxiao Hu, and Fajin Qin. "Ultimate boundedness of impulsive fractional differential equations." Applied Mathematics Letters 62 (December 2016): 110–17. http://dx.doi.org/10.1016/j.aml.2016.06.011.

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28

Ahmed, Hamdy, Mahmoud El-Borai, Hassan El-Owaidy, and Ahmed Ghanem. "Existence Solution and Controllability of Sobolev Type Delay Nonlinear Fractional Integro-Differential System." Mathematics 7, no. 1 (2019): 79. http://dx.doi.org/10.3390/math7010079.

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Fractional integro-differential equations arise in the mathematical modeling of various physical phenomena like heat conduction in materials with memory, diffusion processes, etc. In this manuscript, we prove the existence of mild solution for Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2. We establish the sufficient conditions for the approximate controllability of Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2. In addition, we prove the exact null controllability of Sobolev ty

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29

Stamov, Gani, and Ivanka Stamova. "Impulsive Delayed Lasota–Wazewska Fractional Models: Global Stability of Integral Manifolds." Mathematics 7, no. 11 (2019): 1025. http://dx.doi.org/10.3390/math7111025.

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In this paper we deal with the problems of existence, boundedness and global stability of integral manifolds for impulsive Lasota–Wazewska equations of fractional order with time-varying delays and variable impulsive perturbations. The main results are obtained by employing the fractional Lyapunov method and comparison principle for impulsive fractional differential equations. With this research we generalize and improve some existing results on fractional-order models of cell production systems. These models and applied technique can be used in the investigation of integral manifolds in a wid

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30

Ram Gautam, Ganga, Sandra Pinelas, Manoj Kumar, Namrata Arya, and Jaimala Bishnoi. "On the solution of T−controllable abstract fractional differential equations with impulsive effects." Cubo (Temuco) 25, no. 3 (2023): 363–86. http://dx.doi.org/10.56754/0719-0646.2503.363.

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In this research article, we delimitate the definition of mild solution for abstract fractional differential equations with state-dependent delay (AFDEw/SDD) of order α ∈(1,2) with impulsive effects and compare the solution to the second-order impulsive differential equations. Further, we obtain sufficient conditions of the existence of mild solution for instantaneous and non-instantaneous impulsive fractional functional differential inclusions with state-dependent delay (IFDIw/SDD) using the multi-valued fixed point theory and operator techniques. Furthermore, we study the trajectory controll

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31

Hasan, Sameer Q., and Fatima S. Hussein. "Existence and Stability of Solutions for Bilinear Control System with Rieman-Leovel Initial Condition." Al-Mustansiriyah Journal of Science 28, no. 1 (2017): 118. http://dx.doi.org/10.23851/mjs.v28i1.322.

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In this paper, we shall study the existence of a new class called fractional Caputo type of order sobolev type fractional order differential Equations motion in separable Banach spaces. The class of impulsive nonlinear fractional order bilinear control differential Equations with Riemann Leovel differential initial value studied and discussed also given the important results for the almost periodic mild solution to be sTable by using Menards function and granwal fractional inequality.

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32

Fatima, Rabbiya, Azmat Ullah Khan Niazi, and Hassan Raza. "Novel Insights into Oscillation of Impulsive Fractional Differential Equations with Caputo Derivative." Conclusions in Engineering 1, no. 1 (2025): 44–50. https://doi.org/10.71107/977nnr55.

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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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33

Fu, Xi, and Xiaoyou Liu. "Fractional Differential Equations with Fractional Impulsive and Nonseparated Boundary Conditions." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/364348.

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This paper studies the existence results for nonseparated boundary value problems of fractional differential equations with fractional impulsive conditions. By means of Schaefer fixed point theorem, Banach fixed point theorem, and nonlinear alternative of Leray-Schauder type, some existence results are obtained. Examples are given to illustrate the results.

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34

Zhang, Xianmin, Xianzhen Zhang, Zuohua Liu, Hui Peng, Tong Shu, and Shiyong Yang. "The General Solution of Impulsive Systems with Caputo-Hadamard Fractional Derivative of Orderq∈C (R(q)∈(1,2))." Mathematical Problems in Engineering 2016 (2016): 1–20. http://dx.doi.org/10.1155/2016/8101802.

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Motivated by some preliminary works about general solution of impulsive system with fractional derivative, the generalized impulsive differential equations with Caputo-Hadamard fractional derivative ofq∈C (R(q)∈(1,2)) are further studied by analyzing the limit case (as impulses approach zero) in this paper. The formulas of general solution are found for the impulsive systems.

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35

Babiarz, Artur, and Michał Niezabitowski. "Controllability Problem of Fractional Neutral Systems: A Survey." Mathematical Problems in Engineering 2017 (2017): 1–15. http://dx.doi.org/10.1155/2017/4715861.

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The following article presents recent results of controllability problem of dynamical systems in infinite-dimensional space. Generally speaking, we describe selected controllability problems of fractional order systems, including approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in Hilbert spaces, controllability of nonlinear neutral fractional impulsive differential inclusions in Banach space, controllability for a class of fractional neutral integrodifferential equations with unbounded delay, controllability of neutral frac

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36

Peng, Y. "Second-Order Nonlinear Impulsive Integro-Differential Equations of Mixed Type and Optimal Controls in Fractional Power Spaces." Abstract and Applied Analysis 2010 (2010): 1–16. http://dx.doi.org/10.1155/2010/213503.

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A class of second-order nonlinear impulsive integro-differential equations of mixed type whose principal part is given by time-varying generating operators in fractional power spaces is considered. We introduce the reasonable PC-α-mild solution of second-order nonlinear impulsive integro-differential equations of mixed type and prove its existence. The existence of optimal controls for a Lagrange problem of systems governed by second-order nonlinear impulsive integro-equations of mixed type is also presented. An example is given for demonstration.

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37

Aghili, Arman. "Non-homogeneous impulsive time fractional heat conduction equation." Journal of Numerical Analysis and Approximation Theory 52, no. 1 (2023): 22–33. http://dx.doi.org/10.33993/jnaat521-1316.

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This article provides a concise exposition of the integral transforms and its application to singular integral equation and fractional partial differential equations. The author implemented an analytical technique, the transform method, for solving the boundary value problems of impulsive time fractional heat conduction equation. Integral transforms method is a powerful tool for solving singular integral equations, evaluation of certain integrals involving special functions and solution of partial fractional differential equations. The proposed method is extremely concise, attractive as a math

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Zhang, Xianmin, Praveen Agarwal, Zuohua Liu, Xianzhen Zhang, Wenbin Ding, and Armando Ciancio. "On the fractional differential equations with not instantaneous impulses." Open Physics 14, no. 1 (2016): 676–84. http://dx.doi.org/10.1515/phys-2016-0076.

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AbstractBased on some previous works, an equivalent equations is obtained for the differential equations of fractional-orderq ∈(1, 2) with non-instantaneous impulses, which shows that there exists the general solution for this impulsive fractional-order systems. Next, an example is used to illustrate the conclusion.

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Zhang, Xianmin, Xianzhen Zhang, Zuohua Liu, Wenbin Ding, Hui Cao, and Tong Shu. "On the General Solution of Impulsive Systems with Hadamard Fractional Derivatives." Mathematical Problems in Engineering 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/2814310.

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This paper is concerned with the solution for impulsive differential equations with Hadamard fractional derivatives. The general solution of this impulsive fractional system is found by considering the limit case in which impulses approach zero. Next, an example is provided to expound the theoretical result.

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Hannabou, Mohamed, Khalid Hilal, and Ahmed Kajouni. "Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems." Journal of Mathematics 2020 (November 12, 2020): 1–9. http://dx.doi.org/10.1155/2020/5729128.

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In this paper, a class of nonlocal impulsive differential equation with conformable fractional derivative is studied. By utilizing the theory of operators semigroup and fractional derivative, a new concept on a solution for our problem is introduced. We used some fixed point theorems such as Banach contraction mapping principle, Schauder’s fixed point theorem, Schaefer’s fixed point theorem, and Krasnoselskii’s fixed point theorem, and we derive many existence and uniqueness results concerning the solution for impulsive nonlocal Cauchy problems. Some concrete applications to partial differenti

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41

Odibat, Zaid, Vedat Suat Erturk, Pushpendra Kumar, Abdellatif Ben Makhlouf, and V. Govindaraj. "An Implementation of the Generalized Differential Transform Scheme for Simulating Impulsive Fractional Differential Equations." Mathematical Problems in Engineering 2022 (May 16, 2022): 1–11. http://dx.doi.org/10.1155/2022/8280203.

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In this research study, the generalized differential transform scheme has been applied to simulate impulsive differential equations with the noninteger order. One specific tool of the implemented scheme is that it converts the problems into a recurrence equation that finally leads easily to the solution of the considered problem. The validity and reliability of this method have successfully been accomplished by applying it to simulate the solution of some equations. It is shown that the considered method is very suitable and efficient for solving classes of fractional-order initial value probl

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42

Agarwal, Ravi, Snehana Hristova, and Donal O’Regan. "Caputo fractional differential equations with non-instantaneous impulses and strict stability by Lyapunov functions." Filomat 31, no. 16 (2017): 5217–39. http://dx.doi.org/10.2298/fil1716217a.

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In this paper the statement of initial value problems for fractional differential equations with noninstantaneous impulses is given. These equations are adequate models for phenomena that are characterized by impulsive actions starting at arbitrary fixed points and remaining active on finite time intervals. Strict stability properties of fractional differential equations with non-instantaneous impulses by the Lyapunov approach is studied. An appropriate definition (based on the Caputo fractional Dini derivative of a function) for the derivative of Lyapunov functions among the Caputo fractional

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43

Agarwal, Ravi, Snezhana Hristova, and Donal O'Regan. "Integral presentations of the solution of a boundary value problem for impulsive fractional integro-differential equations with Riemann-Liouville derivatives." AIMS Mathematics 7, no. 2 (2022): 2973–88. http://dx.doi.org/10.3934/math.2022164.

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<abstract><p>Riemann-Liouville fractional differential equations with impulses are useful in modeling the dynamics of many real world problems. It is very important that there are good and consistent theoretical proofs and meaningful results for appropriate problems. In this paper we consider a boundary value problem for integro-differential equations with Riemann-Liouville fractional derivative of orders from $ (1, 2) $. We consider both interpretations in the literature on the presence of impulses in fractional differential equations: With fixed lower limit of the fractional deri

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Karthikeyan, Kulandhaivel, Panjaiyan Karthikeyan, Dimplekumar N. Chalishajar, Duraisamy Senthil Raja та Ponnusamy Sundararajan. "Analysis on ψ-Hilfer Fractional Impulsive Differential Equations". Symmetry 13, № 10 (2021): 1895. http://dx.doi.org/10.3390/sym13101895.

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In this manuscript, we establish the existence of results of fractional impulsive differential equations involving ψ-Hilfer fractional derivative and almost sectorial operators using Schauder fixed-point theorem. We discuss two cases, if the associated semigroup is compact and noncompact, respectively. We consider here the higher-dimensional system of integral equations. We present herewith new theoretical results, structural investigations, and new models and approaches. Some special cases of the results are discussed as well. Due to the nature of measurement of noncompactness theory, there e

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BOHNER, MARTIN, and SNEZHANA HRISTOVA. "Lipschitz Stability for Impulsive Riemann–Liouville Fractional Differential Equations." Kragujevac Journal of Mathematics 48, no. 5 (2024): 723–45. http://dx.doi.org/10.46793/kgjmat2405.723b.

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Initial and impulsive conditions for initial value problems of systems of nonlinear impulsive Riemann–Liouville fractional diﬀerential equations are introduced. The case when the lower limit of the fractional derivative is changed at each time point of the impulses is studied. In the case studied, the solution has a singularity at the initial time and at any point of the impulses. This leads to the need to appropriately generalize the classical concept of Lipschitz stability. Two derivative types of Lyapunov functions are utilized in order to deduce suﬃcient conditions for the new stability co

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46

Yuji Liu and Shimin Li. "Periodic boundary value problems for singular fractional differential equations with impulse effects." Malaya Journal of Matematik 3, no. 04 (2015): 423–90. http://dx.doi.org/10.26637/mjm304/006.

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Abstract:

Firstly by using iterative method, we prove existence and uniqueness of solutions of Cauchy problems of differential equations involving Caputo fractional derivative, Riemann-Liouville and Hadamard fractional derivatives with order $q \in(0,1)$. Then we obtain exact expression of solutions of impulsive fractional differential equations, i.e., exact expression of piecewise continuous solutions. Finally, four classes of integral type periodic boundary value problems of singular fractional differential equations with impulse effects are proposed. Sufficient conditions are given for the existence

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47

Ilolov, M., and Kh S. Kuchakshoev. "Abstract Fractional Integro-Differential Equations with Impulsive Actions." Bulletin of L.N. Gumilyov Eurasian National University. Mathematics. Computer Sciences. Mechanics series 131, no. 2 (2020): 28–34. http://dx.doi.org/10.32523/2616-7182/2020-131-2-28-34.

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Lu, Ziqiang, and Yuanguo Zhu. "Nonlinear impulsive problems for uncertain fractional differential equations." Chaos, Solitons & Fractals 157 (April 2022): 111958. http://dx.doi.org/10.1016/j.chaos.2022.111958.

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Ding, Yali. "Ulam-Hyers stability of fractional impulsive differential equations." Journal of Nonlinear Sciences and Applications 11, no. 08 (2018): 953–59. http://dx.doi.org/10.22436/jnsa.011.08.02.

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Choi, Sung Kyu, and Namjip Koo. "A NOTE ON LINEAR IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS." Journal of the Chungcheong Mathematical Society 28, no. 4 (2015): 583–90. http://dx.doi.org/10.14403/jcms.2015.28.4.583.

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