Journal ArticleDOI
Response to “Comments on the concept of existence of solution for impulsive fractional differential equations [Commun Nonlinear Sci Numer Simul 2014;19:401–3.]”☆
TLDR
This paper is a response to Wang et al. (2014) and presents some scripts to address and discuss the comments, and means a different one, generalized Caputo derivative, by keeping in each impulses which start the lower bounded from zero.About:
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2014-12-01. It has received 50 citations till now. The article focuses on the topics: Fractional calculus & Bounded function.read more
Citations
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Journal ArticleDOI
Existence results for impulsive nonlinear fractional differential equation with mixed boundary conditions
TL;DR: In this paper, the existence and uniqueness of solutions for an impulsive mixed boundary value problem of nonlinear differential equations of fractional order are obtained based on some fixed point theorems.
Journal ArticleDOI
A General Class of Impulsive Evolution Equations
JinRong Wang,Michal Fečkan +1 more
TL;DR: In this paper, a general class of impulsive differential equations is studied, which is more reasonable to show dynamics of evolution processes in Pharmacotherapy, and new concepts of Ulam's type stability and Ulam-Hyers-Rassias stability results on compact and unbounded intervals.
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Nonlocal impulsive fractional differential inclusions with fractional sectorial operators on Banach spaces
TL;DR: Two existence results of PC-mild solutions of impulsive fractional differential inclusions with nonlocal conditions when the linear part is a fractional sectorial operators like in Bajlekova (2001) 1 on Banach spaces are derived.
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On the concept and existence of solutions for fractional impulsive systems with Hadamard derivatives
JinRong Wang,Yuruo Zhang +1 more
TL;DR: A reasonable concept on the solutions of fractional impulsive Cauchy problems with Hadamard derivative and the corresponding fractional integral equations are established and two fundamental existence results are presented by using standard fixed point methods.
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Existence results for impulsive fractional integro-differential equation of mixed type with constant coefficient and antiperiodic boundary conditions
TL;DR: In this paper, the existence and uniqueness of solutions for impulsive fractional integro-differential equation of mixed type with constant coefficient and antiperiodic boundary condition is studied.
References
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A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions
TL;DR: In this article, sufficient conditions for the existence and uniqueness of solutions for various classes of initial and boundary value problems for fractional differential equations and inclusions involving the Caputo fractional derivative are established.
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Erratum to “Experimental Analyses of the Major Parameters Affecting the Intensity of Outbursts of Coal and Gas”
TL;DR: Here, the authors correct the errors made in Table 3 and equation (5) in the paper titled “Experimental Analyses of the Major Parameters Affecting the Intensity of Outbursts of Coal and Gas.”
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On the concept and existence of solution for impulsive fractional differential equations
TL;DR: In this paper, the existence of a solution for impulsive Cauchy problems with fractional derivative is investigated and sufficient conditions for existence of the solutions are established by applying fixed point methods.
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Ulam’s type stability of impulsive ordinary differential equations☆
TL;DR: The authors introduced four Ulam's type stability concepts for impulsive ODEs, and applied the integral inequality of Gronwall type for piecewise continuous functions to obtain type stability results.
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Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations
Bashir Ahmad,S. Sivasundaram +1 more
TL;DR: In this paper, the existence results for a two-point boundary value problem involving nonlinear impulsive hybrid differential equation of fractional order q ∈ ( 1, 2 ] were discussed.