scholarly journals On the General Solution of Impulsive Systems with Hadamard Fractional Derivatives

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Xianmin Zhang ◽  
Xianzhen Zhang ◽  
Zuohua Liu ◽  
Wenbin Ding ◽  
Hui Cao ◽  
...  
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Theoretical Result ◽  
Fractional Derivatives ◽  
Impulsive Differential Equations ◽  
Limit Case ◽  
Impulsive Systems ◽  
Fractional System ◽  
Approach Zero

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.

scholarly journals The General Solution of Impulsive Systems with Caputo-Hadamard Fractional Derivative of Orderq∈C  (R(q)∈(1,2))

2016 ◽  
Vol 2016 ◽  
pp. 1-20 ◽  
Author(s):  
Xianmin Zhang ◽  
Xianzhen Zhang ◽  
Zuohua Liu ◽  
Hui Peng ◽  
Tong Shu ◽  
...  
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Impulsive Differential Equations ◽  
Impulsive System ◽  
Limit Case ◽  
Impulsive Systems ◽  
Hadamard Fractional Derivative ◽  
Approach Zero

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.

scholarly journals The general solution for impulsive differential equations with Riemann-Liouville fractional-order q ∈ (1,2)

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Xianmin Zhang ◽  
Praveen Agarwal ◽  
Zuohua Liu ◽  
Hui Peng
Keyword(s):  
Approximate Solution ◽  
General Solution ◽  
Differential Equations ◽  
Fractional Order ◽  
Impulsive Differential Equations ◽  
Impulsive System ◽  
Limit Case ◽  
Approach Zero

AbstractIn this paper we consider the generalized impulsive system with Riemann-Liouville fractional-order q ∈ (1,2) and obtained the error of the approximate solution for this impulsive system by analyzing of the limit case (as impulses approach zero), as well as find the formula for a general solution. Furthermore, an example is given to illustrate the importance of our results.

scholarly journals The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous Impulses

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Xianzhen Zhang ◽  
Zuohua Liu ◽  
Hui Peng ◽  
Xianmin Zhang ◽  
Shiyong Yang
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
General Solution ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Order System ◽  
Impulsive Systems ◽  
Fractional Differential ◽  
Noninstantaneous Impulses

Based on some recent works about the general solution of fractional differential equations with instantaneous impulses, a Caputo-Hadamard fractional differential equation with noninstantaneous impulses is studied in this paper. An equivalent integral equation with some undetermined constants is obtained for this fractional order system with noninstantaneous impulses, which means that there is general solution for the impulsive systems. Next, an example is given to illustrate the obtained result.

scholarly journals The general solution of impulsive systems with Riemann-Liouville fractional derivatives

2016 ◽  
Vol 14 (1) ◽  
pp. 1125-1137 ◽  
Author(s):  
Xianmin Zhang ◽  
Wenbin Ding ◽  
Hui Peng ◽  
Zuohua Liu ◽  
Tong Shu
Keyword(s):  
General Solution ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Fractional Order System ◽  
Order System ◽  
Impulsive Effect ◽  
Impulsive Systems ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Formula Of General Solution

AbstractIn this paper, we study a kind of fractional differential system with impulsive effect and find the formula of general solution for the impulsive fractional-order system by analysis of the limit case (as impulse tends to zero). The obtained result shows that the deviation caused by impulses for fractional-order system is undetermined. An example is also provided to illustrate the result.

scholarly journals On the concept of general solution for impulsive differential equations of fractional-order q ∈ (2,3)

2016 ◽  
Vol 14 (1) ◽  
pp. 452-473 ◽  
Author(s):  
Xianmin Zhang ◽  
Tong Shu ◽  
Zuohua Liu ◽  
Wenbin Ding ◽  
Hui Peng ◽  
...  
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Fractional Order ◽  
Impulsive Differential Equations ◽  
Formula Of General Solution

AbstractIn this paper, we find the formula of general solution for a generalized impulsive differential equations of fractional-order q ∈ (2, 3).

scholarly journals On Nonlinear Forced Impulsive Differential Equations under Canonical and Non-Canonical Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2066
Author(s):  
Shyam Sundar Santra ◽  
Hammad Alotaibi ◽  
Samad Noeiaghdam ◽  
Denis Sidorov
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Impulsive System ◽  
Bounded Solutions ◽  
Oscillatory Behaviour ◽  
Impulsive Systems ◽  
Forcing Term

This study is connected with the nonoscillatory and oscillatory behaviour to the solutions of nonlinear neutral impulsive systems with forcing term which is studied for various ranges of of the neutral coefficient. Furthermore, sufficient conditions are obtained for the existence of positive bounded solutions of the impulsive system. The mentioned example shows the feasibility and efficiency of the main results.

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