EXISTENCE OF SOLUTIONS OF ABSTRACT FRACTIONAL IMPULSIVE SEMILINEAR EVOLUTION EQUATIONS

By Krishnan Balachandran, S. Kiruthika. 2010

113 citations recorded by the source corpus.

In this paper we prove the existence of solutions of fractional impulsive semilinear evolution equations in Banach spaces. A nonlocal Cauchy problem is discussed for the evolution equations. The results are obtained using fractional calculus and fixed point theorems. An example is provided to illustrate the theory.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b9e24b9d1f24af14fd02e7dcc572349e5807e8a0

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In Applied Mathematics

1. Jinrong Wang
2. Yong Zhou
3. Michal Feckan
4. Donal O'Regan
5. Ravi P. Agarwal
6. Snezhana G. Hristova
7. Wei Wei
8. Juan Trujillo

In Modeling and Simulation

1. Jinrong Wang
2. Yong Zhou
3. Michal Feckan
4. Donal O'Regan
5. Ravi P. Agarwal
6. Snezhana G. Hristova
7. Juan Trujillo
8. Wei Wei

In Numerical Analysis

1. Jinrong Wang
2. Yong Zhou
3. Donal O'Regan
4. Ravi P. Agarwal
5. Michal Feckan
6. Snezhana G. Hristova
7. Wei Wei
8. Juan Trujillo

Citations in the corpus

• 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”
• A survey on impulsive fractional differential equations (2016, methodology): “This approach is used in several papers (see for example, [1, 3, 6, 7, 19]).”
• The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces (2010, background): “Balachandran and Kiruthika [26] discussed the nonlocal Cauchy problem with an impulsive condition for semilinear fractional differential equations, whereas Chang and Nieto [27] studied the same problem for neutral integrodifferential equations via fractional operators.”
• 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:”
• A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations (2016, methodology): “In [20], the authors pointed out that the formula, based on (V1) of solutions for IFrDE in [1], [3], [10] is incorrect and gave a new formula using approach (V2).”