Fractional Tarig transform and Mittag - Leffler function
DOI :
https://doi.org/10.5269/bspm.v35i2.29388Résumé
In the present paper the Tarig transform of fractional order is studied by employing Mittag - Leffler function. Properties of Tarig transform are proved using the same fractional Tarig transform.
Références
1. Tarig M. Elzaki and Salih M. Elzaki, . New integral transform "Tarig Transform" and system of integro differential equations, Elixir Appl. Math. 57 (2013), 13982 - 13985.
2. Tarig M. Elzaki and Salih M. Elzaki, Application of Tarig transform to Integral and Integro-Differential Equations, Elixir Appl. Math. 57 (2013), 13978 - 13981.
3. Tarig M. Elzaki and Salih M. Elzaki, Application of new transform "Tarig transform" to partial differential equations, Elixir Appl. Math. 42 (2012), 6369 - 6372.
4. Tarig M. Elzaki and Salih M Elzaki, On the relationship between Laplace and new integral transform "Tarig transform", Elixir Appl. Math. 36 (2011), 3230 - 3233.
5. A.Erdelyi, (ed.) Higher Transcendental Functions, Vol. 1, McGraw Hill, New York. (1955)
6. G. Jumarie, Laplace’s transform of fractional order via the Mittag – Leffler function and modified Riemann – Liouville derivative, Appl. Math. Letters, 22 (2009) 1659 – 1664.
7. G. Jumarie, Fourier’s transform of fractional order via the Mittag – Leffler function and modified Riemann – Liouville derivative, J. Appl. Math. & Informatics, 26 (5-6), (2008) 1101 - 1121.
8. Adem Kilicman, and Omer Altun, Some remarks on the Fractional Sumudu transform and Applications, Appl. Math. Inf. Sci. 8 (6) (2014), 2881 - 2888.
9. Muhammet Kurulay, and Mustafa Bayram, Some properties of the Mittag – Leffler functions and their relation with the Wright functions, Advances in Difference Equation, 2012, (2012) 181 – 188.
10. Deshna Loonker, Fractional Natural Transform and the Mittag - Leffler function, J. Indian Acad. Math. 37 (2) (2015) ( To Appear)
11. Deshna Loonker and P. K. Banerji, Distributional Abel integral equation for distributional Tarig transform, Int. J. Appl. Math. 27 (3) (2014), 245 - 254
12. Deshna Loonker and P. K. Banerji, Tarig transformation for Distribution and Boehmian Spaces, Indian Journal of Mathematics Research 2 (1) (2014), 1-8
13. Deshna Loonker and P. K Banerji, On Tarig Fractional Differintegral Transform on Distribution Spaces, Pure and Applied Mathematics Letters 2 (2014), 19-25
14. K. S. Miller, and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons Inc., New York (1993)
15. G. Mittag – Leffler, Sur la nouvelle fonction , Comptes Rendus Hebdomadaires Des Seances Del Academie Des Sciences, Paris 2 (137), (1903) 554 – 558.
16. K. B. Oldham, and J. Spanier, The Fractional Calculus, Academic Press, New York. (1974)
17. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego. (1999)
18. S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach Science Publishers, London.(1987)
2. Tarig M. Elzaki and Salih M. Elzaki, Application of Tarig transform to Integral and Integro-Differential Equations, Elixir Appl. Math. 57 (2013), 13978 - 13981.
3. Tarig M. Elzaki and Salih M. Elzaki, Application of new transform "Tarig transform" to partial differential equations, Elixir Appl. Math. 42 (2012), 6369 - 6372.
4. Tarig M. Elzaki and Salih M Elzaki, On the relationship between Laplace and new integral transform "Tarig transform", Elixir Appl. Math. 36 (2011), 3230 - 3233.
5. A.Erdelyi, (ed.) Higher Transcendental Functions, Vol. 1, McGraw Hill, New York. (1955)
6. G. Jumarie, Laplace’s transform of fractional order via the Mittag – Leffler function and modified Riemann – Liouville derivative, Appl. Math. Letters, 22 (2009) 1659 – 1664.
7. G. Jumarie, Fourier’s transform of fractional order via the Mittag – Leffler function and modified Riemann – Liouville derivative, J. Appl. Math. & Informatics, 26 (5-6), (2008) 1101 - 1121.
8. Adem Kilicman, and Omer Altun, Some remarks on the Fractional Sumudu transform and Applications, Appl. Math. Inf. Sci. 8 (6) (2014), 2881 - 2888.
9. Muhammet Kurulay, and Mustafa Bayram, Some properties of the Mittag – Leffler functions and their relation with the Wright functions, Advances in Difference Equation, 2012, (2012) 181 – 188.
10. Deshna Loonker, Fractional Natural Transform and the Mittag - Leffler function, J. Indian Acad. Math. 37 (2) (2015) ( To Appear)
11. Deshna Loonker and P. K. Banerji, Distributional Abel integral equation for distributional Tarig transform, Int. J. Appl. Math. 27 (3) (2014), 245 - 254
12. Deshna Loonker and P. K. Banerji, Tarig transformation for Distribution and Boehmian Spaces, Indian Journal of Mathematics Research 2 (1) (2014), 1-8
13. Deshna Loonker and P. K Banerji, On Tarig Fractional Differintegral Transform on Distribution Spaces, Pure and Applied Mathematics Letters 2 (2014), 19-25
14. K. S. Miller, and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons Inc., New York (1993)
15. G. Mittag – Leffler, Sur la nouvelle fonction , Comptes Rendus Hebdomadaires Des Seances Del Academie Des Sciences, Paris 2 (137), (1903) 554 – 558.
16. K. B. Oldham, and J. Spanier, The Fractional Calculus, Academic Press, New York. (1974)
17. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego. (1999)
18. S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach Science Publishers, London.(1987)
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2016-03-21
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Research Articles
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