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Journal of Linear and Topological Algebra (JLTA)
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Volume Volume 08 (2019)
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Elomari, M., Melliani, S., Taqbibt, A., Chadli, S. (2019). Solving fractional evolution problem in Colombeau algebra by mean generalized fixed point. Journal of Linear and Topological Algebra (JLTA), 08(01), 71-84.
M. Elomari; S. Melliani; A. Taqbibt; S. Chadli. "Solving fractional evolution problem in Colombeau algebra by mean generalized fixed point". Journal of Linear and Topological Algebra (JLTA), 08, 01, 2019, 71-84.
Elomari, M., Melliani, S., Taqbibt, A., Chadli, S. (2019). 'Solving fractional evolution problem in Colombeau algebra by mean generalized fixed point', Journal of Linear and Topological Algebra (JLTA), 08(01), pp. 71-84.
Elomari, M., Melliani, S., Taqbibt, A., Chadli, S. Solving fractional evolution problem in Colombeau algebra by mean generalized fixed point. Journal of Linear and Topological Algebra (JLTA), 2019; 08(01): 71-84.

Solving fractional evolution problem in Colombeau algebra by mean generalized fixed point

Article 7, Volume 08, Issue 01, Winter 2019, Page 71-84  XML PDF (173.14 K)
Document Type: Research Paper
Authors
M. Elomari email ; S. Melliani; A. Taqbibt; S. Chadli
Department of Mathematics, Faculty of Sciences and Technics, Beni-Mellal, Morocco
Abstract
‎The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$‎ ‎for the real $q\in (0,1)$ with the initial value $u(0)=u_{0}\in\tilde{\R}$‎, ‎where $\tilde{\R}$ is the set of all generalized real numbers and $A$ is an operator defined from $\mathcal G$ into itself‎. Here the Caputo fractional derivative $D^{q}_c$ is used instead of the usual derivative. The introduction of locally convex spaces is to use their topology in order to define generalized semigroups and generalized fixed points, then to show our requested result.
Keywords
Colombeau algebra; locally convexe space; generalized semigroup; generalized fixed point
Main Subjects
Ordinary differential equations
References
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[2] J. F. Colombeau, Elementary Introduction to New Generalized Function, North Holland, Amsterdam, 1985.

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[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.

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[10] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Bull. Amer. Math. Soc. (N.S.) 12 (1985), —.

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