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Saïd Abbas, Wafaa A. Albarakati, Mouffak Benchohra, Mohamed Abdalla Darwish, Eman M. Hilal (2015)
Annales Polonici Mathematici
We discuss the existence of solutions and Ulam's type stability concepts for a class of partial functional fractional differential inclusions with noninstantaneous impulses and a nonconvex valued right hand side in Banach spaces. An example is provided to illustrate our results.
Pagnini, Gianni (2011)
Fractional Calculus and Applied Analysis
MSC 2010: 34A08 (main), 34G20, 80A25The application of Fractional Calculus in combustion science to model the evolution in time of the radius of an isolated premixed flame ball is highlighted. Literature equations for premixed flame ball radius are rederived by a new method that strongly simplifies previous ones. These equations are nonlinear time-fractional differential equations of order 1/2 with a Gaussian underlying diffusion process. Extending the analysis to self-similar anomalous diffusion...
Liu, Yanqin, Xin, Baogui (2011)
Advances in Difference Equations [electronic only]
Bartosz Bandrowski, Anna Karczewska, Piotr Rozmej (2010)
International Journal of Applied Mathematics and Computer Science
This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a large-scale system of linear equations with a non-symmetric matrix is solved with the use of the iterative GMRES method.
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