Solving fractional evolution problem in Colombeau algebra by mean generalized fixed point
Subject Areas : Ordinary differential equationsM. Elomari 1 , S. Melliani 2 , A. Taqbibt 3 , S. Chadli 4
1 - Department of Mathematics, Faculty of Sciences and Technics, Beni-Mellal, Morocco
2 - Department of Mathematics, Faculty of Sciences and Technics, Beni-Mellal, Morocco
3 - Department of Mathematics, Faculty of Sciences and Technics, Beni-Mellal, Morocco
4 - Department of Mathematics, Faculty of Sciences and Technics, Beni-Mellal, Morocco
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[1] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Inter. J. Math. & Math. Sci. 29 (9) (2002), 531-536.
[2] J. F. Colombeau, Elementary Introduction to New Generalized Function, North Holland, Amsterdam, 1985.
[3] J. F. Colombeau, New Generalized Function and Multiplication of Distribution, North Holland, Amsterdam, 1984.
[4] M. Grosser, M. Kunzinger, M. Oberguggenberger, R. Steinbauer, Geometric Theory of Generalized Functions with Applications to General Relativity, Mathematics and its Applications 537, Dordrecht, 2001.
[5] R. Hermann, M. Oberguggenberger, Ordinary differential equations and generalized functions, in: Nonlinear Theory of Generalized Functions, Chapman & Hall, 1999.
[6] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier B.V, Netherlands, 2006.
[7] J. A. Marti, Fixed points in algebras of generalized functions and applications, HAL Id: hal-01231272.
[8] R. Metzler, J. Klafter, The random walks guide to anomalous diffusion: a fractional dynamics approach, Physics Reports. 339 (2000), 1-77.
[9] M. Oberguggenberger, Multiplication of Distributions and Applications to Partial Differential Equations, Pitman Research Notes in Mathematics, 1992.
[10] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Bull. Amer. Math. Soc. (N.S.) 12 (1985), —.