Solving Generalized Fractional Schrodinger’s Equation by Mean Generalized Fixed Point

Melliani, S.; Elomari, M.; Chadli, L. S.

doi:10.1007/978-3-030-26149-8_7

S. Melliani⁵,
M. Elomari⁵ &
L. S. Chadli⁵

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 243))

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Abstract

The present paper is devoted to the existence and uniqueness results of the generalized fractional Schrodinger’s equation

$$\begin{aligned} {\left\{ \begin{array}{ll} \frac{1}{i}\partial ^{\alpha }_{t}u(t,x)-\triangle u(t,x)+v(x)u(t,x)=0, \quad x\in \mathbb {R},\ t\ge 0 \\ v(x)=\delta (x), \quad u(0,x)=\delta (x) \end{array}\right. } \end{aligned}$$

by using the generalized fixed point.

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References

Branciari, A.: A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int. J. Math. Math. Sci. 29(9), 531–536 (2002)
Article MathSciNet Google Scholar
Colombeau, J.F.: New Generalized Function and Multiplication of Distribution. North Holland, Amsterdam (1984)
MATH Google Scholar
Colombeau, J.F.: Elementary Introduction to New Generalized Function. North Holland, Amsterdam (1985)
MATH Google Scholar
Grosser, M., Kunzinger, M., Oberguggenberger, M., Steinbauer, R.: Geometric Theory of Generalized Functions with Applications to General Relativity, Mathematics and its Applications, vol. 537. Kluwer Academic Publishers, Dordrecht (2001)
Book Google Scholar
Hermann, R., Oberguggenberger, M.: Ordinary differential equations and generalized functions. Non- linear Theory of Generalized Functions, pp. 85–98. Chapman & Hall, Boca Raton (1999)
MATH Google Scholar
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier B.V, Netherlands (2006)
MATH Google Scholar
Oberguggenberger, M.: Multiplication of Distributions and Applications to Partial Differential Equations. Pitman Research Notes in Mathematics. Longman Scientific & Technical, Harlow (1992)
MATH Google Scholar
Marti, J.A.: Fixed points in algebras of generalized functions and applications, HAL Id: hal-01231272
Google Scholar
Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, vol. 44. Springer, New York (1983)
Book Google Scholar

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Authors and Affiliations

Sultan Moulay Slimane University, BP 523, Beni Mellal, Morocco
S. Melliani, M. Elomari & L. S. Chadli

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S. Melliani
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M. Elomari
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L. S. Chadli
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Correspondence to S. Melliani .

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Editors and Affiliations

Department of Mathematics, Moulay Ismail University, Zitoune Meknès, Morocco
El Hassan Zerrik
Department of Mathematics, Sultan Moulay Slimane University, Beni Mellal, Morocco
Said Melliani
Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico
Oscar Castillo

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Melliani, S., Elomari, M., Chadli, L.S. (2020). Solving Generalized Fractional Schrodinger’s Equation by Mean Generalized Fixed Point. In: Zerrik, E., Melliani, S., Castillo, O. (eds) Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications. Studies in Systems, Decision and Control, vol 243. Springer, Cham. https://doi.org/10.1007/978-3-030-26149-8_7

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DOI: https://doi.org/10.1007/978-3-030-26149-8_7
Published: 27 August 2019
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-26148-1
Online ISBN: 978-3-030-26149-8
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