The fundamental solutions for fractional evolution equations of parabolic type
By Mahmoud M. El-Borai. 2004
135 citations recorded by the source corpus.
The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is given as an application.
Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/09af4f97d5322033275a398f0b431f934bc15652
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In Applied Mathematics
- Nazim Idrisoglu Mahmudov
- Yongxiang Li
- Jinrong Wang
- Michal Feckan
- Pengyu Chen
- Yong Zhou
- Xuping Zhang
- Amar Debbouche
In Modeling and Simulation
- Nazim Idrisoglu Mahmudov
- Yongxiang Li
- Jinrong Wang
- Michal Feckan
- Pengyu Chen
- Yong Zhou
- Xuping Zhang
- Amar Debbouche
In Numerical Analysis
- Nazim Idrisoglu Mahmudov
- Jinrong Wang
- Michal Feckan
- Yongxiang Li
- Yong Zhou
- Pengyu Chen
- Amar Debbouche
- Xuping Zhang
Citations in the corpus
- WEAK ALMOST PERIODIC AND OPTIMAL MILD SOLUTIONS OF FRACTIONAL EVOLUTION EQUATIONS (2009, background): “2) According to [5, 6, 7, 8, 9], a solution of equation (1.”
- Approximate Controllability of Fractional Sobolev-Type Evolution Equations in Banach Spaces (2013, methodology): “We refer the reader to ElBorai [3, 4], Balachandran and Park [5], Zhou and Jiao [6, 7] Hernández et al.”
- A blowup alternative result for fractional nonautonomous evolution equation of Volterra type (2018, background): “For more details, see [2, 4, 6, 8, 9, 11, 12], [18]-[22], [28]-[32] and the references therein for more comments and citations.”
- Controllability of Sobolev type fractional evolution systems (2014, background): “For more interesting theory results and scientific applications of fractional differential equations, we cite the monographs [2, 3, 4, 5, 6], the research papers [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31] and the references therein.”
- On the new concept of solutions and existence results for impulsive fractional evolution equations (2011, background): “A pioneering work on some probability densities and fundamental solutions of Caputo fractional evolution equations has been reported by El-Borai [28, 29].”