On the fractional differential equations with not instantaneous impulses

Abstract Based 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.

[1]  Dumitru Baleanu,et al.  On exact traveling-wave solutions for local fractional Korteweg-de Vries equation. , 2016, Chaos.

[2]  B. Ahmad,et al.  Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional or , 2011 .

[3]  Tong Shu,et al.  The General Solution of Impulsive Systems with Caputo-Hadamard Fractional Derivative of Order , 2016 .

[4]  Zhanbing Bai,et al.  Existence results for the three-point impulsive boundary value problem involving fractional differential equations , 2010, Comput. Math. Appl..

[5]  Ivanka M. Stamova,et al.  Stability analysis of impulsive functional systems of fractional order , 2014, Commun. Nonlinear Sci. Numer. Simul..

[6]  Tong Shu,et al.  On the concept of general solution for impulsive differential equations of fractional-order q ∈ (2,3) , 2016 .

[7]  S. Ntouyas,et al.  Boundary value problems for impulsive multi-order Hadamard fractional differential equations , 2015 .

[8]  Changjin Xu,et al.  Mild solution of fractional order differential equations with not instantaneous impulses , 2015 .

[9]  S. Sivasundaram,et al.  Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations , 2009 .

[10]  Bashir Ahmad,et al.  Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions , 2011, Comput. Math. Appl..

[11]  Hari M. Srivastava,et al.  A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach , 2016, Appl. Math. Comput..

[12]  S. Abbas,et al.  EXISTENCE THEORY FOR IMPULSIVE PARTIAL HYPERBOLIC FUNCTIONAL DIFFERENTIAL EQUATIONS INVOLVING THE CAPUTO FRACTIONAL DERIVATIVE , 2010 .

[13]  Yong Zhou,et al.  On the concept and existence of solution for impulsive fractional differential equations , 2012 .

[14]  Moufiak Benchohra,et al.  IMPULSIVE PARTIAL HYPERBOLIC FUNCTIONAL DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER WITH STATE-DEPENDENT DELAY , 2010 .

[15]  Bashir Ahmad,et al.  On Caputo–Hadamard type fractional impulsive hybrid systems with nonlinear fractional integral conditions , 2016 .

[16]  S. Lai,et al.  The global solution and blow-up phenomena to a modified Novikov equation , 2014 .

[17]  D. Baleanu,et al.  On fractional neutral integro-differential systems with state-dependent delay and non-instantaneous impulses , 2015 .

[18]  Tong Shu,et al.  The general solution for impulsive differential equations with Hadamard fractional derivative of order q∈(1,2)$q \in(1, 2)$ , 2016 .

[19]  Xianmin Zhang,et al.  On the concept of general solution for impulsive differential equations of fractional order q ∈(0, 1) , 2014, Appl. Math. Comput..

[20]  Tian Liang Guo,et al.  Impulsive fractional partial differential equations , 2015, Appl. Math. Comput..

[21]  Na Xu,et al.  Existence and properties of meromorphic solutions of some q-difference equations , 2015, Advances in Difference Equations.

[22]  J. A. Tenreiro Machado,et al.  Nonlinear dynamics for local fractional Burgers’ equation arising in fractal flow , 2016 .

[23]  S. Sivasundaram,et al.  Existence of solutions for impulsive integral boundary value problems of fractional order , 2010 .

[24]  N. Ford,et al.  Analysis of Fractional Differential Equations , 2002 .

[25]  M. Arjunan,et al.  About the Existence Results of Fractional Neutral Integrodifferential Inclusions with State-Dependent Delay in Frechet Spaces , 2016 .

[26]  P. Agarwal,et al.  The general solution for impulsive differential equations with Riemann-Liouville fractional-order q ∈ (1,2) , 2015 .

[27]  Tong Shu,et al.  On the General Solution of Impulsive Systems with Hadamard Fractional Derivatives , 2016 .

[28]  S. Ntouyas,et al.  Impulsive fractional boundary-value problems with fractional integral jump conditions , 2014 .

[29]  Xianmin Zhang On impulsive partial differential equations with Caputo-Hadamard fractional derivatives , 2016 .

[30]  M. Arjunan,et al.  Exact controllability of fractional neutral , 2016 .

[31]  Donal O'Regan,et al.  On a new class of abstract impulsive differential equations , 2012 .

[32]  Xianmin Zhang The general solution of differential equations with Caputo-Hadamard fractional derivatives and impulsive effect , 2015 .

[33]  Ravi P. Agarwal,et al.  Darboux problem for impulsive partial hyperbolic differential equations of fractional order with variable times and infinite delay , 2010 .

[34]  Haibo Chen,et al.  Some results on impulsive boundary value problem for fractional differential inclusions , 2011 .

[35]  Xi Fu,et al.  On a new class of impulsive fractional evolution equations , 2015, Advances in Difference Equations.

[36]  Mouffak Benchohra,et al.  IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS IN , 2010 .

[37]  D. Baleanu,et al.  Exact controllability of fractional neutral integro-differential systems with state-dependent delay in Banach spaces , 2015 .

[38]  Mouffak Benchohra,et al.  Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order , 2010 .