Nonlocal Cauchy problem for abstract fractional semilinear evolution equations

By Krishnan Balachandran, Jong‐Yeoul Park. 2009

161 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/1af4520026e6a45584fb9a71f9228e2686e02b7a

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In Applied Mathematics

1. Jinrong Wang
2. Yong Zhou
3. Yongxiang Li
4. Pengyu Chen
5. Rathinasamy Sakthivel
6. Wei Wei
7. Juan Trujillo
8. Yong Ren

In Modeling and Simulation

1. Jinrong Wang
2. Yongxiang Li
3. Yong Zhou
4. Pengyu Chen
5. Wei Wei
6. Juan Trujillo
7. Rathinasamy Sakthivel
8. Yong Ren

Citations in the corpus

• The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces (2010, background): “Recently N'Guerekata [23] and Balachandran and Park [24] investigated the existence of solutions of fractional abstract differential equations with nonlocal initial condition.”
• Existence Results for Fractional Order Semilinear Integro-Differential Evolution Equations with Infinite Delay (2010, methodology): “Recently, Balachandran and Park [2] proved the existence and uniqueness of solutions to the following fractional order semilinear evolution equations by means of the Banach contraction principle and the Krasnoselskii fixed point theorem: { Dqu(t)−A(t)u(t) = f (t, u(t)) , t ∈ J := [0, T ], u(0) + g(u”
• Existence and uniqueness of mild solutions for semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays (2009, background): “Recently, Balachandran and Park [ 2 ] proved the existence and uniqueness of solutions to the following fractional semilinear evolution equations by means of the Banach contraction principle and Krasnoselskii’s fixed point theorem: �”
• Existence of Solutions for Impulsive Anti-periodic Boundary Value Problems of Fractional Order (2011, unknown): “For examples and details, see [1-3, 5, 7, 10, 15-16, 18-19, 23-24, 26] and the references therein.”
• EXISTENCE OF SOLUTIONS OF ABSTRACT FRACTIONAL IMPULSIVE SEMILINEAR EVOLUTION EQUATIONS (2010, background): “Mophou and N’Guérékata [22, 23, 24] and Balachandran and Park [5] discussed the existence of solutions of abstract fractional differential equations with nonlocal initial conditions.”
• 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 mild solutions for fractional evolution equations with mixed monotone nonlocal conditions (2013, methodology): “Recently, Wang and Yang [16]; Wang, Xiao, and Liang [17]; Li, Liang, and Xu [18]; Zhou and Jiao [19]; Wang et al. [20]; Balachandran and Park [21]; Balachandran and Trujillo [22]; Balachandran, Kiruthika, and Trujillo [23]; Chang, Kavitha, and Mallika Arjunan [24]; and Tatar [25] studied nonlocal pr”