ANALYTICAL RESOLUTION OF THE CAUCHY PROBLEM OF A DIFFUSION EQUATION WITH A FRACTIONAL TIME DERIVATIVE.

Rasolomampiandry Gilbert; Ravaliminoarimalalason T.B; RasoanoavyF; RandimbindrainibeF

ANALYTICAL RESOLUTION OF THE CAUCHY PROBLEM OF A DIFFUSION EQUATION WITH A FRACTIONAL TIME DERIVATIVE.

December 2018

Vol-4, Issue-6

Paper ID: 9326

ISSN: 2395-4396

Downloads: 0

Abstract & Details

Research Area

Sciences engineering

Keywords

Fractional derivative Generalized functions Mittag-Leffler function.

Abstract

In this paper, we will present a method of analytical resolution of a fractional time derivative diffusion equation with an initial condition. Spectral theory of the operators, Hilbert space, some properties of Mittag-Leffler function, Fourier transformation of the generalized functions are main tools for this resolution.

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Author Information

#	Name	Institute / Affiliation
1	Rasolomampiandry Gilbert	Laboratoire de recherche Sciences Cognitives et Applications (LR - SCA) Ecole Doctorale en Sciences et Techniques de l’Ingénierie et de l’Innovation (ED - STII) Ecole Supérieure Polytechnique Antananarivo (ESPA) - Université d’Antananarivo BP 1500, Ankatso – Antananarivo 101 - Madagascar
2	Ravaliminoarimalalason T.B	Laboratoire de recherche Sciences Cognitives et Applications (LR - SCA) Ecole Doctorale en Sciences et Techniques de l’Ingénierie et de l’Innovation (ED - STII) Ecole Supérieure Polytechnique Antananarivo (ESPA) - Université d’Antananarivo BP 1500, Ankatso – Antananarivo 101 - Madagascar
3	RasoanoavyF	Laboratoire de recherche Sciences Cognitives et Applications (LR - SCA) Ecole Doctorale en Sciences et Techniques de l’Ingénierie et de l’Innovation (ED - STII) Ecole Supérieure Polytechnique Antananarivo (ESPA) - Université d’Antananarivo BP 1500, Ankatso – Antananarivo 101 - Madagascar
4	RandimbindrainibeF	Laboratoire de recherche Sciences Cognitives et Applications (LR - SCA) Ecole Doctorale en Sciences et Techniques de l’Ingénierie et de l’Innovation (ED - STII) Ecole Supérieure Polytechnique Antananarivo (ESPA) - Université d’Antananarivo BP 1500, Ankatso – Antananarivo 101 - Madagascar

How to Cite

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APA Style

Gilbert, Rasolomampiandry, T.B, Ravaliminoarimalalason, RasoanoavyF, & RandimbindrainibeF (2018). ANALYTICAL RESOLUTION OF THE CAUCHY PROBLEM OF A DIFFUSION EQUATION WITH A FRACTIONAL TIME DERIVATIVE.. International Journal of Advance Research and Innovative Ideas In Education, 4(6), 473-479.

MLA Style

Gilbert, Rasolomampiandry, et al. "ANALYTICAL RESOLUTION OF THE CAUCHY PROBLEM OF A DIFFUSION EQUATION WITH A FRACTIONAL TIME DERIVATIVE.." International Journal of Advance Research and Innovative Ideas In Education, vol. 4, no. 6, 2018, pp. 473-479.

IEEE Style

Rasolomampiandry Gilbert, Ravaliminoarimalalason T.B, RasoanoavyF, and RandimbindrainibeF, "ANALYTICAL RESOLUTION OF THE CAUCHY PROBLEM OF A DIFFUSION EQUATION WITH A FRACTIONAL TIME DERIVATIVE.," International Journal of Advance Research and Innovative Ideas In Education, vol. 4, no. 6, pp. 473-479, 2018.

Vancouver Style

Gilbert Rasolomampiandry, T.B Ravaliminoarimalalason, RasoanoavyF, RandimbindrainibeF. ANALYTICAL RESOLUTION OF THE CAUCHY PROBLEM OF A DIFFUSION EQUATION WITH A FRACTIONAL TIME DERIVATIVE.. International Journal of Advance Research and Innovative Ideas In Education. 2018;4(6):473-479.

Harvard Style

Gilbert, Rasolomampiandry, T.B, Ravaliminoarimalalason, RasoanoavyF, & RandimbindrainibeF (2018) 'ANALYTICAL RESOLUTION OF THE CAUCHY PROBLEM OF A DIFFUSION EQUATION WITH A FRACTIONAL TIME DERIVATIVE.', International Journal of Advance Research and Innovative Ideas In Education, 4(6), pp. 473-479.

Chicago Style

Gilbert, Rasolomampiandry, et al. "ANALYTICAL RESOLUTION OF THE CAUCHY PROBLEM OF A DIFFUSION EQUATION WITH A FRACTIONAL TIME DERIVATIVE.." International Journal of Advance Research and Innovative Ideas In Education 4, no. 6 (2018): 473-479.

Turabian Style

Gilbert, Rasolomampiandry, et al. "ANALYTICAL RESOLUTION OF THE CAUCHY PROBLEM OF A DIFFUSION EQUATION WITH A FRACTIONAL TIME DERIVATIVE.." International Journal of Advance Research and Innovative Ideas In Education 4, no. 6 (2018): 473-479.