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Operational Methods For Sub - Ballistic And Coupled Fractional PDEs

Year 2018, Volume: 6 Issue: 1, 42 - 48, 15.04.2018

Abstract

In this article, it is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve a certain system of fractional PDEs and a variety of Lamb - Bateman singular integral equation. The Lamb - Bateman singular integral equation was introduced to study the solitary wave diffraction. It may be concluded that the integral transforms and exponential operators are effective methods for solving integral equations and fractional linear equations with non-constant coefficients.

References

  • [1] A.Aghili. New results involving Airy polynomials, fractional calculus and solution to generalized heat equation. New trends in mathematical sciences. Vol. 3, issue 4, Dec. 2015.pp 133-143.
  • [2] A. Aghili, Fractional Black - Scholes equation, International Journal of Financial Engineering, 4(1), (2017) 1750004 (15 pages)© World Scientific Publishing Company.
  • [3] A.Aghili, H.Zeinali: New Trends In Laplace Type Integral Transforms With Applications. Bol. Soc. Paran. Mat. Vol. 35,1. (2017), 174 - 191.
  • [4] A.Apelblat. Laplace transforms and their applications, Nova science publishers, Inc, New York, 2012.
  • [5] D.Babusci, G.Dattoli, D.Sacchetti. The Lamb - Bateman integral equation and the fractional derivatives.Fractional calculus and applied analysis.vol 14, no 2, 2011.pp 317 - 320.
  • [6] G.Dattoli. Operational methods, fractional perators and special polynomials. Applied Mathematics and computations.141 (2003) pp 151-159.
  • [7] G.Dattoli, H.M.Srivastava,K.V.Zhukovsky. Operational methods and differential equations to initial value problems. Applied Mathematics and computations.184 (2007) pp 979-1001.
  • [8] I. Podlubny. Fractional Differential Equations, Academic Press, San Diego, CA,1999.
  • [9] F.Usta, H.Budak, M.Z.Sarikaya, Yang - Laplace transform method for local fractional Volterra and Abel’s integro - differential equations. www.reaearchgate.net/publication/316923150.
  • [10] F.Usta, Numerical solution of fractional elliptic PDEs by collocation method, Appl. Appl. Math.,2017,12(1), 470 - 478.
  • [11] X.Y. Yang, D.Baleanu, H.M.Srivastava, Local fractional integral transforms and their applications, Elsevier/Academic Press,Amesterdam,(2016).
Year 2018, Volume: 6 Issue: 1, 42 - 48, 15.04.2018

Abstract

References

  • [1] A.Aghili. New results involving Airy polynomials, fractional calculus and solution to generalized heat equation. New trends in mathematical sciences. Vol. 3, issue 4, Dec. 2015.pp 133-143.
  • [2] A. Aghili, Fractional Black - Scholes equation, International Journal of Financial Engineering, 4(1), (2017) 1750004 (15 pages)© World Scientific Publishing Company.
  • [3] A.Aghili, H.Zeinali: New Trends In Laplace Type Integral Transforms With Applications. Bol. Soc. Paran. Mat. Vol. 35,1. (2017), 174 - 191.
  • [4] A.Apelblat. Laplace transforms and their applications, Nova science publishers, Inc, New York, 2012.
  • [5] D.Babusci, G.Dattoli, D.Sacchetti. The Lamb - Bateman integral equation and the fractional derivatives.Fractional calculus and applied analysis.vol 14, no 2, 2011.pp 317 - 320.
  • [6] G.Dattoli. Operational methods, fractional perators and special polynomials. Applied Mathematics and computations.141 (2003) pp 151-159.
  • [7] G.Dattoli, H.M.Srivastava,K.V.Zhukovsky. Operational methods and differential equations to initial value problems. Applied Mathematics and computations.184 (2007) pp 979-1001.
  • [8] I. Podlubny. Fractional Differential Equations, Academic Press, San Diego, CA,1999.
  • [9] F.Usta, H.Budak, M.Z.Sarikaya, Yang - Laplace transform method for local fractional Volterra and Abel’s integro - differential equations. www.reaearchgate.net/publication/316923150.
  • [10] F.Usta, Numerical solution of fractional elliptic PDEs by collocation method, Appl. Appl. Math.,2017,12(1), 470 - 478.
  • [11] X.Y. Yang, D.Baleanu, H.M.Srivastava, Local fractional integral transforms and their applications, Elsevier/Academic Press,Amesterdam,(2016).
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Arman Aghili

Publication Date April 15, 2018
Submission Date November 14, 2017
Published in Issue Year 2018 Volume: 6 Issue: 1

Cite

APA Aghili, A. (2018). Operational Methods For Sub - Ballistic And Coupled Fractional PDEs. Konuralp Journal of Mathematics, 6(1), 42-48.
AMA Aghili A. Operational Methods For Sub - Ballistic And Coupled Fractional PDEs. Konuralp J. Math. April 2018;6(1):42-48.
Chicago Aghili, Arman. “Operational Methods For Sub - Ballistic And Coupled Fractional PDEs”. Konuralp Journal of Mathematics 6, no. 1 (April 2018): 42-48.
EndNote Aghili A (April 1, 2018) Operational Methods For Sub - Ballistic And Coupled Fractional PDEs. Konuralp Journal of Mathematics 6 1 42–48.
IEEE A. Aghili, “Operational Methods For Sub - Ballistic And Coupled Fractional PDEs”, Konuralp J. Math., vol. 6, no. 1, pp. 42–48, 2018.
ISNAD Aghili, Arman. “Operational Methods For Sub - Ballistic And Coupled Fractional PDEs”. Konuralp Journal of Mathematics 6/1 (April 2018), 42-48.
JAMA Aghili A. Operational Methods For Sub - Ballistic And Coupled Fractional PDEs. Konuralp J. Math. 2018;6:42–48.
MLA Aghili, Arman. “Operational Methods For Sub - Ballistic And Coupled Fractional PDEs”. Konuralp Journal of Mathematics, vol. 6, no. 1, 2018, pp. 42-48.
Vancouver Aghili A. Operational Methods For Sub - Ballistic And Coupled Fractional PDEs. Konuralp J. Math. 2018;6(1):42-8.
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