scholarly journals The general solution for impulsive differential equations with Hadamard fractional derivative of order q ∈ ( 1 , 2 ) $q \in(1, 2)$

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Xianmin Zhang ◽  
Tong Shu ◽  
Hui Cao ◽  
Zuohua Liu ◽  
Wenbin Ding
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Impulsive Differential Equations ◽  
Hadamard Fractional Derivative

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 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 Some Antiperiodic Boundary Value Problem for Nonlinear Fractional Impulsive Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xianghu Liu ◽  
Yanfang Li
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Existence Of Solutions ◽  
Integral Formula ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Uniqueness Of Solutions ◽  
Liouville Fractional Derivative

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.

scholarly journals General solution of Bernoulli and Riccati fractional differential equations based on conformable fractional derivative

2017 ◽  
Vol 6 (2) ◽  
pp. 49 ◽  
Author(s):  
Zainab Ayati ◽  
Jafar Biaar ◽  
Mousa Ilei
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Ordinary Differential Equations ◽  
Fractional Differential Equations ◽  
Riccati Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Conformable Fractional Derivative ◽  
Numerical Examples ◽  
Fractional Differential

This paper is aimed to develop two well-known nonlinear ordinary differential equations, Bernoulli and Riccati equations to fractional form. General solution to fractional differential equations are detected, based on conformable fractional derivative. For each equation, numerical examples are presented to illustrate the proposed approach.  

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 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.

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