Öz
Kaynakça
- [1] L. Debnath and D. Bhatta, Integral Transforms and Their Applications 2nd Edition, Chapman and Hall CRC, Boca Raton, London and New York, 2007.
- [2] A.N. Dernek and F. Aylıkçı, Identities for the $\mathcal{L}_{n}$-Transform, the $\mathcal{L}_{2n}$-Transform, and the $\mathcal{P}_{2n}$-Transform and Their Applications, Journal of Inequaities and Special Functions, 5 (4), 1–16, 2014.
- [3] A.N. Dernek and F. Aylıkçı, Some Results on the $\mathcal{P}_{\nu,2n}$, $\mathcal{K}_{\nu,n}$, $\mathcal{H}_{\nu,n}$ Integral trans- forms, Turkish J. Math. 41, 337–349, 2017.
- [4] A. Dernek, N. Dernek and O. Yürekli, Identities for the Henkel Transform and Their Applications, J. Math. Anal. Appl. 354, 165–176, 2009.
- [5] A.N. Dernek, V. Kurt, Y. Şimşek and O. Yürekli, A generalization of Widder Potential Transform and Applications, Integral Transforms Spec. Funct. 22, 391–401, 2011.
- [6] A.N. Dernek, H.M. Srivasta and O. Yürekli, Parseval-Goldstein Type Identities In- volving The $\mathcal{L}_{4}$ Transform and $\mathcal{P}_{4}$ Transform and Their Applications, Integral Trans- forms Spec. Funct. 18, (6), 397–408, 2007.
- [7] A. Erdelyi, W. Magnus, F. Oberhettinger and F. Tricomi, Tables of Integral Trans- forms Vol: 1, Mc-Graw-Hill Book Company, New York, Toronto and London, 1954.
- [8] A. Erdelyi, W. Magnus, F. Oberhettinger and F. Tricomi, Tables of Integral Trans- forms Vol: 2, Mc-Graw-Hill Book Company, New York, Toronto and London, 1954.
- [9] I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York, 1996.
- [10] C. Li, D. Qian and Y. Chen, On Riemann Liouville and Caputo Derivatives, Discrete Dyn. Nat. Soc. 2011, 2011.
- [11] K.S. Miller and B. Ross, An Introduction to Fractional Calculus and Fractional Dif- ferential Equations, John Wiley-Interscience Publication, New York, Toronto, Singa- pore, 1993.
- [12] I. Podlubny, An Introduction to Fractional Derivatives, Fractional Differential Equa- tions, to Methods of their Solution and Some of their Applications, Academic Press, San Diego and London, 1990.
- [13] D.V. Widder, An Introduction to Transform Theory, Academic Press, New York, 1971.
- [14] O. Yürekli and I. Sadek, A Parseval-Goldstein Type Theorem on the Widder Potential Transform and Its Applications, International J. Math. Math. Sci. 14 (3), 517–524, 1991.
- [15] O. Yürekli, Identities on Fractional Integrals and Various Integral Transforms, Appl. Math. Comput. 187, 559–566, 2007.
Öz
In this paper, we introduce various theorems that associate the generalized Riemann-Liouville fractional integral operator and the generalized Weyl fractional integral operator with some well-known integral transforms including generalized Laplace transform, Widder potential transform, generalized Widder transform, Hankel transform and Bessel transform. We evaluate certain integrals of some elementary functions and some special functions as applications of these theorems and their results.
Anahtar Kelimeler
Riemann-Liouville fractional integral Weyl fractional integral fractional derivatives Laplace transform Widder potential transform Hankel transform Bessel transform error function exponential integral function
Kaynakça
- [1] L. Debnath and D. Bhatta, Integral Transforms and Their Applications 2nd Edition, Chapman and Hall CRC, Boca Raton, London and New York, 2007.
- [2] A.N. Dernek and F. Aylıkçı, Identities for the $\mathcal{L}_{n}$-Transform, the $\mathcal{L}_{2n}$-Transform, and the $\mathcal{P}_{2n}$-Transform and Their Applications, Journal of Inequaities and Special Functions, 5 (4), 1–16, 2014.
- [3] A.N. Dernek and F. Aylıkçı, Some Results on the $\mathcal{P}_{\nu,2n}$, $\mathcal{K}_{\nu,n}$, $\mathcal{H}_{\nu,n}$ Integral trans- forms, Turkish J. Math. 41, 337–349, 2017.
- [4] A. Dernek, N. Dernek and O. Yürekli, Identities for the Henkel Transform and Their Applications, J. Math. Anal. Appl. 354, 165–176, 2009.
- [5] A.N. Dernek, V. Kurt, Y. Şimşek and O. Yürekli, A generalization of Widder Potential Transform and Applications, Integral Transforms Spec. Funct. 22, 391–401, 2011.
- [6] A.N. Dernek, H.M. Srivasta and O. Yürekli, Parseval-Goldstein Type Identities In- volving The $\mathcal{L}_{4}$ Transform and $\mathcal{P}_{4}$ Transform and Their Applications, Integral Trans- forms Spec. Funct. 18, (6), 397–408, 2007.
- [7] A. Erdelyi, W. Magnus, F. Oberhettinger and F. Tricomi, Tables of Integral Trans- forms Vol: 1, Mc-Graw-Hill Book Company, New York, Toronto and London, 1954.
- [8] A. Erdelyi, W. Magnus, F. Oberhettinger and F. Tricomi, Tables of Integral Trans- forms Vol: 2, Mc-Graw-Hill Book Company, New York, Toronto and London, 1954.
- [9] I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York, 1996.
- [10] C. Li, D. Qian and Y. Chen, On Riemann Liouville and Caputo Derivatives, Discrete Dyn. Nat. Soc. 2011, 2011.
- [11] K.S. Miller and B. Ross, An Introduction to Fractional Calculus and Fractional Dif- ferential Equations, John Wiley-Interscience Publication, New York, Toronto, Singa- pore, 1993.
- [12] I. Podlubny, An Introduction to Fractional Derivatives, Fractional Differential Equa- tions, to Methods of their Solution and Some of their Applications, Academic Press, San Diego and London, 1990.
- [13] D.V. Widder, An Introduction to Transform Theory, Academic Press, New York, 1971.
- [14] O. Yürekli and I. Sadek, A Parseval-Goldstein Type Theorem on the Widder Potential Transform and Its Applications, International J. Math. Math. Sci. 14 (3), 517–524, 1991.
- [15] O. Yürekli, Identities on Fractional Integrals and Various Integral Transforms, Appl. Math. Comput. 187, 559–566, 2007.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 6 Şubat 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 49 Sayı: 1 |