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In this paper, we prove the existence and uniqueness of solution to the impulsive fuzzy functional differential equations under generalized Hukuhara differentiability via the principle of contraction mappings. Some examples are pr...
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In this paper, we prove the existence and uniqueness of solution to the impulsive fuzzy functional differential equations under generalized Hukuhara differentiability via the principle of contraction mappings. Some examples are provided to illustrate the result.
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In this paper, we provide the formulas of general solution for some impulsive differential equations of fractional-order q is an element of(1, 2). (C) 2015 Elsevier Inc. All rights reserved.
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In this paper we mainly study a kind of fractional differential equations with not instantaneous impulses, and find the equivalent equations of the impulsive system. The obtained result discovers that there exist general solution ...
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In this paper we mainly study a kind of fractional differential equations with not instantaneous impulses, and find the equivalent equations of the impulsive system. The obtained result discovers that there exist general solution for the impulsive system. Next, an example is given to illustrate the obtained result.
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In this paper, for impulsive differential equations with fractional-order q?(0,1), we show that the formula of solutions in cited papers are incorrect. Secondly, we find out a formula of the general solution for impulsive Cauchy p...
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In this paper, for impulsive differential equations with fractional-order q?(0,1), we show that the formula of solutions in cited papers are incorrect. Secondly, we find out a formula of the general solution for impulsive Cauchy problem with Caputo fractional derivative q?(0,1). Further, for a kind of impulsive fractional differential equations system with special initial value, we come to an existence result for it by applying fixed point methods.
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This paper mainly focuses on the non-uniqueness of solution to the initial value problem (IVP) of impulsive fractional differential equations (IFrDE) with Caputo-Katugampola derivative (of order q is an element of (1, 2)). The sys...
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This paper mainly focuses on the non-uniqueness of solution to the initial value problem (IVP) of impulsive fractional differential equations (IFrDE) with Caputo-Katugampola derivative (of order q is an element of (1, 2)). The system of impulsive higher order fractional differential equations may involve two different kinds of impulses, and the obtained result shows that its equivalent integral equations include two arbitrary constants, which means that its solution is non-unique. Next, two numerical examples are used to show the non-uniqueness of solution for the IVP of IFrDE.
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In this paper, we established the exploitation of impulsive harvesting single autonomous population model by Logistic equation. By some special methods, we analysis the impulsive harvesting population equation and obtain existence...
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In this paper, we established the exploitation of impulsive harvesting single autonomous population model by Logistic equation. By some special methods, we analysis the impulsive harvesting population equation and obtain existence, the explicit expression and global attractiveness of impulsive periodic solutions for constant yield harvest and proportional harvest. Then, we choose the maximum sustainable yield as management objective, and investigate the optimal impulsive harvesting policies respectively. The optimal harvest effort that maximizes the sustainable yield per unit time, the corresponding optimal population levels are determined. At last, we point out that the continuous harvesting policy is superior to the impulsive harvesting policy, however, the latter is more beneficial in realistic operation. (C) 2003 Elsevier Science Ltd. All rights reserved. [References: 10]
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We study the existence of solutions for a class of impulsive differential equations. Our technical framework allows us to study partial differential equations with impulsive conditions involving partial derivatives and nonlinear e...
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We study the existence of solutions for a class of impulsive differential equations. Our technical framework allows us to study partial differential equations with impulsive conditions involving partial derivatives and nonlinear expressions of the solution. Some applications to impulsive partial differential equations are presented.
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Sufficient conditions are found for oscillation of the bounded solutions of a class of impulsive differential equations of second order with retarded argument and fixed moments of impulse effect. Some asymptotic properties of the ...
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Sufficient conditions are found for oscillation of the bounded solutions of a class of impulsive differential equations of second order with retarded argument and fixed moments of impulse effect. Some asymptotic properties of the nonoscillating solutions of such equations are investigated.
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Consider the second-order impulsive ordinary differential equation (r(t)(x'(t)~σ)' + f(t,x(t)) = 0, t ≥ t_0, t ≠ t_k, k = 1,2,…, x(t_k~+) = g_k(x(t_k)), x'(t_k~+) = h_k(x'(t_k)), k = 1,2,…, where 0 ≤ t_0 < t_1 < … < t_k < … with lim_(k→+∞) t_k = +∞, σ is any quotient of positive odd integers. We obtain some sufficient conditions ensuring that all solutions of (E) oscillate....
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Consider the second-order impulsive ordinary differential equation (r(t)(x'(t)~σ)' + f(t,x(t)) = 0, t ≥ t_0, t ≠ t_k, k = 1,2,…, x(t_k~+) = g_k(x(t_k)), x'(t_k~+) = h_k(x'(t_k)), k = 1,2,…, where 0 ≤ t_0 < t_1 < … < t_k < … with lim_(k→+∞) t_k = +∞, σ is any quotient of positive odd integers. We obtain some sufficient conditions ensuring that all solutions of (E) oscillate.
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In this paper, the non-uniqueness of solution is mainly considered to the initial value problem (IVP) for the system of impulsive fractional differential equations (IFrDE) with Caputo-Katugampola derivative. The IVP for IFrDE with...
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In this paper, the non-uniqueness of solution is mainly considered to the initial value problem (IVP) for the system of impulsive fractional differential equations (IFrDE) with Caputo-Katugampola derivative. The IVP for IFrDE with Caputo-Katugampola derivative is equivalent to the integral equations with an arbitrary constant, which means that the solution is non-unique. Finally, a numerical example is provided to show the main result.
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