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On some generalized integral transforms and Parseval-Goldstein type relations

Year 2021, Volume: 50 Issue: 2, 526 - 540, 11.04.2021
https://doi.org/10.15672/hujms.595919

Abstract

In the present article, using the generalized Bessel-Maitland transform, the Laplace transform and the other known transforms, authors obtain new Parseval-Goldstein type relations. Using these relations, some generalized integrals involving Fox-Wright functions are evaluated. Illustrative examples are also given.

References

  • [1] D. Albayrak, A. Dernek, F. Uçar and N. Dernek, Theorems on the Generalized Bessel- Maitland Integral Transform and its Applications, Math. Meth. Appl. Sci. 1–15, 2020.
  • [2] D. Brown, N. Dernek and O. Yürekli, Identities for the exponential integral and the complementary error transforms, Appl. Math. Comput. 182, 1377–1384, 2006.
  • [3] L. Debnath and D. Bhatta, Integral Transforms and Their Applications, Chapman and Hall/CRC, 2006.
  • [4] N. Dernek, H.M. Srivastava and O. Yürekli, Parseval-Goldstein Type Identities In- volving the L4-Transform and the P4-Transform and Their Applications, Integral Transforms Spec. Funct. 18 (6), 397–408, 2007.
  • [5] A. Erdelyi, Table of Integral Transforms, Vol I, Mcgraw Hill, New York, 1954.
  • [6] A. Erdelyi, Table of Integral Transforms, Vol II, Mcgraw Hill, New York, 1954.
  • [7] A. Erdelyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Higher Transcendental Functions, Vol.I,II, McGraw-Hill, New York Toronto and London, 1954. Reprinted: Krieger, Melbourne-Florida 1981.
  • [8] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley-Interscience, 1993.
  • [9] F. Oberhettinger, Tables of Mellin Transforms, Springer-Verlag, New York, 1974.
  • [10] K.B. Oldham, J. Spanier and J. Myland, An atlas of functions, 2ed., Springer, 2010.
  • [11] I. Podlubny, An Introduction to Fractional Derivatives, Fractional Differantial Equa- tions, to Methods of their Solution and Some of their Applications, Academic Press, San Diego and London, 1990.
  • [12] M. Singh, M.A. Khan and A.H. Khan, On Some Properties of a Generalization of Bessel-Maitland Function, International Journal of Mathematics Trend and Tecnol- ogy, 14 (1), 46–54, 2014.
  • [13] O. Yürekli, A Parseval-type theorem applied to certain integral transforms, IMA J. Appl. Math. 42, 241–249, 1989.
  • [14] O. Yürekli, A Theorem on the Generalized Stieltjes Transform and its Applications, J. Math. Anal. Appl. 168, 63–71, 1992.
  • [15] D.V. Widder, The Stieltjes Transform, Trans. Amer. Math. Soc. 43 (1), 7–60, 1938.
  • [16] E.M. Wright, The asymptotic expansion of the generalized hypergeometric function, Proc. London Math. Soc. 10 (4), 286–293, 1935.
Year 2021, Volume: 50 Issue: 2, 526 - 540, 11.04.2021
https://doi.org/10.15672/hujms.595919

Abstract

References

  • [1] D. Albayrak, A. Dernek, F. Uçar and N. Dernek, Theorems on the Generalized Bessel- Maitland Integral Transform and its Applications, Math. Meth. Appl. Sci. 1–15, 2020.
  • [2] D. Brown, N. Dernek and O. Yürekli, Identities for the exponential integral and the complementary error transforms, Appl. Math. Comput. 182, 1377–1384, 2006.
  • [3] L. Debnath and D. Bhatta, Integral Transforms and Their Applications, Chapman and Hall/CRC, 2006.
  • [4] N. Dernek, H.M. Srivastava and O. Yürekli, Parseval-Goldstein Type Identities In- volving the L4-Transform and the P4-Transform and Their Applications, Integral Transforms Spec. Funct. 18 (6), 397–408, 2007.
  • [5] A. Erdelyi, Table of Integral Transforms, Vol I, Mcgraw Hill, New York, 1954.
  • [6] A. Erdelyi, Table of Integral Transforms, Vol II, Mcgraw Hill, New York, 1954.
  • [7] A. Erdelyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Higher Transcendental Functions, Vol.I,II, McGraw-Hill, New York Toronto and London, 1954. Reprinted: Krieger, Melbourne-Florida 1981.
  • [8] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley-Interscience, 1993.
  • [9] F. Oberhettinger, Tables of Mellin Transforms, Springer-Verlag, New York, 1974.
  • [10] K.B. Oldham, J. Spanier and J. Myland, An atlas of functions, 2ed., Springer, 2010.
  • [11] I. Podlubny, An Introduction to Fractional Derivatives, Fractional Differantial Equa- tions, to Methods of their Solution and Some of their Applications, Academic Press, San Diego and London, 1990.
  • [12] M. Singh, M.A. Khan and A.H. Khan, On Some Properties of a Generalization of Bessel-Maitland Function, International Journal of Mathematics Trend and Tecnol- ogy, 14 (1), 46–54, 2014.
  • [13] O. Yürekli, A Parseval-type theorem applied to certain integral transforms, IMA J. Appl. Math. 42, 241–249, 1989.
  • [14] O. Yürekli, A Theorem on the Generalized Stieltjes Transform and its Applications, J. Math. Anal. Appl. 168, 63–71, 1992.
  • [15] D.V. Widder, The Stieltjes Transform, Trans. Amer. Math. Soc. 43 (1), 7–60, 1938.
  • [16] E.M. Wright, The asymptotic expansion of the generalized hypergeometric function, Proc. London Math. Soc. 10 (4), 286–293, 1935.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Durmuş Albayrak This is me 0000-0002-3786-5900

Nese Dernek 0000-0003-2148-2152

Publication Date April 11, 2021
Published in Issue Year 2021 Volume: 50 Issue: 2

Cite

APA Albayrak, D., & Dernek, N. (2021). On some generalized integral transforms and Parseval-Goldstein type relations. Hacettepe Journal of Mathematics and Statistics, 50(2), 526-540. https://doi.org/10.15672/hujms.595919
AMA Albayrak D, Dernek N. On some generalized integral transforms and Parseval-Goldstein type relations. Hacettepe Journal of Mathematics and Statistics. April 2021;50(2):526-540. doi:10.15672/hujms.595919
Chicago Albayrak, Durmuş, and Nese Dernek. “On Some Generalized Integral Transforms and Parseval-Goldstein Type Relations”. Hacettepe Journal of Mathematics and Statistics 50, no. 2 (April 2021): 526-40. https://doi.org/10.15672/hujms.595919.
EndNote Albayrak D, Dernek N (April 1, 2021) On some generalized integral transforms and Parseval-Goldstein type relations. Hacettepe Journal of Mathematics and Statistics 50 2 526–540.
IEEE D. Albayrak and N. Dernek, “On some generalized integral transforms and Parseval-Goldstein type relations”, Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 2, pp. 526–540, 2021, doi: 10.15672/hujms.595919.
ISNAD Albayrak, Durmuş - Dernek, Nese. “On Some Generalized Integral Transforms and Parseval-Goldstein Type Relations”. Hacettepe Journal of Mathematics and Statistics 50/2 (April 2021), 526-540. https://doi.org/10.15672/hujms.595919.
JAMA Albayrak D, Dernek N. On some generalized integral transforms and Parseval-Goldstein type relations. Hacettepe Journal of Mathematics and Statistics. 2021;50:526–540.
MLA Albayrak, Durmuş and Nese Dernek. “On Some Generalized Integral Transforms and Parseval-Goldstein Type Relations”. Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 2, 2021, pp. 526-40, doi:10.15672/hujms.595919.
Vancouver Albayrak D, Dernek N. On some generalized integral transforms and Parseval-Goldstein type relations. Hacettepe Journal of Mathematics and Statistics. 2021;50(2):526-40.