IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES

By Mouffak Benchohra, Djamila Seba, Bel Abb. 2009

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This paper is devoted to study the existence of solutions for a class of initial value problems for impulsive fractional differential equations involving the Caputo fractional derivative in a Banach space. The arguments are based upon

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/36f375f54abc5c8bc18dd084791bc4617b968c0b

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

Non-instantaneous impulses in Caputo fractional differential equations (2017, background): “There are also many recent contributions on fractional order differential equations with instantaneous impulses (see, for example, [4], [5], [9], [16], [17], [20], [24], [32], [40], [43]); - non-instantaneous impulses - an impulsive action, starting abruptly at a fixed point and its action continues”
A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations (2016, background): “There are mainly two viewpoints: (V1) Using the classical Caputo derivative and working in each subinterval, determined by the impulses (see, for example, [1], [2], [10], [12], [13]).”
A survey on impulsive fractional differential equations (2016, methodology): “This approach is used in several papers (see for example, [1, 3, 6, 7, 19]).”
Study in Fractional Differential Equations by Means of Topological Degree Methods (2012, methodology): “[6, 7] extended the existence results for solutions of the fractional NCP (1) and fractional ICP (3) to some abstract fractional semilinear evolution equations with bounded linear operators by using the known Banach contraction principle and Krasnoselskii theorem; Benchohra and Seba [12] extended th”
EXISTENCE OF SOLUTIONS OF ABSTRACT FRACTIONAL IMPULSIVE SEMILINEAR EVOLUTION EQUATIONS (2010, background): “Recently Benchohra and Slimani [6,7] discussed the existence and uniqueness of solutions of impulsive fractional differential equations and Ahmad and Sivasundaram [1] discussed the existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations.”
Ulam–Hyers stability of impulsive integrodifferential equations with Riemann–Liouville boundary conditions (2020, unknown): “The monographs [5, 6, 16, 38] treated fractional differential equations with instantaneous impulses of the following form:”
The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces (2010, background): “Benchohra and Seba [25] studied the existence problem for impulsive fractional differential equations in Banach spaces.”