Mild solution of fractional order differential equations with not instantaneous impulses

Keywords

Mathematics, Impulse (physics), Boundary value problem, Mathematical analysis, Order (exchange)

References

• Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)Anatoly A. Kilbas, H. M. Srivastava, Juan J. Trujillo — 2006
• Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and MediaVasilij E. Tarasov — 2011
• The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo TypeKai Diethelm — 2010
• Theory of Fractional Dynamic SystemsV. Lakshmikantham, S. Leela, J. Vasundhara Devi — 2009
• An Introduction to the Fractional Calculus and Fractional Differential EquationsKenneth S. Miller, Bertram Ross — 1993
• Theory and Applications of Fractional Differential EquationsA. Kilbas, H. Srivastava, J. Trujillo — 2006
• Analysis of Fractional Differential EquationsKai Diethelm, Neville J. Ford — 2002
• A class of fractional evolution equations and optimal controlsJinRong Wang, Yong Zhou — 2011
• The existence of mild solutions for impulsive fractional partial differential equationsXiao‐Bao Shu, Yongzeng Lai, Yuming Chen — 2011
• Existence of solutions for semi-linear abstract differential equations with not instantaneous impulsesMichelle Pierri, Donal O’Regan, Vanessa Rolnik — 2013
• Impulsive fractional functional differential equationsTian Liang Guo, Wei Jiang — 2012
• On a new class of abstract impulsive differential equationsEduardo Hernández, Donal O’Regan — 2012
• The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delayXianmin Zhang, Xiyue Huang, Zuohua Liu — 2010
• A class of fractional delay nonlinear integrodifferential controlled systems in Banach spacesJinRong Wang, Yong Zhou, W. Wei — 2011
• A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and InclusionsRavi P. Agarwal, Mouffak Benchohra, Samira Hamani — 2010
• Existence and uniqueness of mild solutions to impulsive fractional differential equationsGisèle Mophou — 2010
• Nonlocal Cauchy problem for fractional evolution equationsYong Zhou, Feng Jiao — 2010
• Controllability of fractional-order impulsive neutral functional infinite delay integrodifferential systems in Banach spacesZhixin Tai, Xingcheng Wang — 2009
• Existence results for fractional order functional differential equations with infinite delayMouffak Benchohra, Johnny Henderson, Sotiris K. Ntouyas — 2008
• Existence of positive solution for some class of nonlinear fractional differential equationsShuqin Zhang — 2003

Cited by

• The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous ImpulsesXianzhen Zhang, Zuohua Liu, Hui Peng — 2017
• On General Solution for Fractional Differential Equations with Not Instantaneous ImpulsesXianmin Zhang, Xianmin Zhang, Xianzhen Zhang — 2017
• Nonlinear fractional boundary value problem with not instantaneous impulseVidushi Gupta, Jaydev Dabas — 2017
• A class of fractional order systems with not instantaneous impulsesXianmin Zhang — 2017
• Noninstantaneous Impulsive Fractional Quantum Hahn Integro-Difference Boundary Value ProblemsSurang Sitho, Chayapat Sudprasert, Sotiris K. Ntouyas — 2020
• A new method for searching the integral solution of system of Riemann-Liouville fractional differential equations with non-instantaneous impulsesXianmin Zhang — 2021
• Existence results of noninstantaneous impulsive fractional integro-differential equationHaribhai R. Kataria, Prakashkumar H. Patel, Vishant Shah — 2020
• Optimal control problem for fractional stochastic delayed systems with noninstantaneous impulsesSurendra Kumar, Anjali Upadhyay — 2021
• Non-Instantaneous Impulsive Boundary Value Problems Containing Caputo Fractional Derivative of a Function with Respect to Another Function and Riemann-Stieltjes Fractional Integral Boundary ConditionsSuphawat Asawasamrit, Yasintorn Thadang, Sotiris K. Ntouyas — 2021
• On the mixed fractional quantum and Hadamard derivatives for impulsive boundary value problemsSomboon Niyoom, Sotiris K. Ntouyas, Chayapat Sudprasert — 2021
• Impulsive fractional order integrodifferential equation via fractional operatorsAhmad Al-Omari, Hanan Al-Saadi — 2023
• Non-instantaneous Impulses in Differential Equations with Caputo Fractional DerivativesR. Agarwal, S. Hristova, D. O’Regan — 2017

Related papers

• Fractional Calculus Approach to Dynamic Problems of Viscoelastic MaterialsNobuyuki Shimizu, Wei Zhang — 1999
• Properties of Vector-Valued τ τ -Discrete Fractional Calculus and its Connection with Caputo Fractional DerivativesYong‐Kui Chang, Rodrigo Ponce — 2023
• Unexpected behavior of Caputo fractional derivativeLucas Kenjy Bazaglia Kuroda, Arianne Vellasco Gomes, Robinson Tavoni — 2017
• Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculusJi‐Huan He, S.K. Elagan, Z.B. Li — 2012
• Comparative Analysis and Definitions of Fractional DerivativesAdil Khurshaid, Hajra Khurshaid — 2023
• Some applications of extended calculus to non-Newtonian flow in pipesMario F. Letelier, Juan S. Stockle — 2021
• Numerical Simulation and Experimental Studies on Impulse of Flexible ExplosiveDengwang Wang — 2011
• Existence of solutions of BVPs for impulsive fractional Langevin equations involving Caputo fractional derivativesYuji Liu, Ravi P. Agarwal — 2019