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Non-homogenous KdV and coupled sub-ballistic fractional PDEs

Year 2017, Volume: 5 Issue: 3, 107 - 117, 01.07.2017

Arman Aghili

Abstract

In this article, the author solved certain system of time fractional equations using integral transforms. Transform method is a powerful tool for solving singular integral equations, evaluation of certain integrals and solution to partial fractional differential equations. The result reveals that the transform method is very convenient and effective.

Keywords

Caputo fractional derivative nonhomogeneous time fractional heat equation Laplace transform Fourier transform

References

  • A. Aghili, H. Zeinali. Advances in Laplace type integral transforms with applications. Indian Journal of Science and Technology, Vol 7(6), 877–890, June 2014.
  • A. Aghili, H. Zeinali. Solution to time fractional wave equation in the presence of friction via integral transform. Communications on applied nonlinear analysis, Vol.21, No.2, pp.67-88, 2014.
  • A. Aghili; M. R. Masomi. Integral transform method for solving different F.S.I.Es and P.F.D.Es. Konuralp Journal of Mathematics, Volume 2, No. 1 pp. 45-62, 2014.
  • T.M. Atanackovic , B.Stankovic. Dynamics of a visco -elastic rod of Fractional derivative type, Z. Angew. Math. Mech., 82(6), (2002) 377-386.
  • T. M. Atanackovic , B.Stankovic. On a system of differential equations with fractional derivatives arising in rod theory. Journal of Physics A: Mathematical and General, 37, No 4, 1241-1250 (2004).
  • D. G. Duffy. Transform methods for solving partial differential equations. Chapman and Hall/CRC, 2004.
  • R. S. Dahiya . M . Vinayagamoorthy.Laplace transfom pairs of n-dimensions and heat conduction problem. Math. Comput. Modelling vol. 13.No. 10 , pp,35-50.
  • V.A. Ditkin. A.P.Prudnikov. Operational calculus In two variables and its application ,Pergamon Press, New York,1962.
  • V. W. Ekman . On the influence of the earth’s rotation on ocean currents. Ark. Math. Astr. Fys. 2. No 1905.
  • A. A. Kilbass ,J. J. Trujillo. Differential equation of fractional order: methods, results and problems. II, Appl. Anal, 81(2), (2002)435-493.
  • Y. Luchko, H. M. Srivastava. The exact solution of certain differential equations of fractional Order by using operational calculus.Comput.Math.Appl.29 (1995)73-85.
  • S. Miller, B. Ross. An introduction to fractional differential equations,Wiley, NewYork.
  • K. B. Oldham, J. Spanier.The Fractional calculus,Academic Press, NewYork, 1974.
  • K. B. Oldham, J. Spanier, Fractional calculus and its applications, Bull.Inst.Politech.. Sect. I, 24 (28)(3-4), (1978) 29-34.
  • I. Podlubny, The Laplace transform method for linear differential equations of fractional order, Slovak Academy of sciences. Slovak Republic, 1994.
  • I. Podlubny. Fractional differential equations, Academic Press, San Diego, CA,1999.
  • G.E.Roberts, H. Kaufman. Table of Laplace transforms, Philadelphia; W.B.Saunders Co. 1966.
  • G. Samko , A. Kilbas. O. Marchiev. Fractional Integrals and derivatives theory and applications. Gordon and Breach,Amesterdam,1993.
  • W. Schneider, W. Wyss. Fractional diffusion and wave equations. J. Math. Phys.30(1989)134-144.
  • B.A.Stankovic. system of partial differential equations with fractional derivatives,Math. Vesnik, 3-4(54), (2002) 187-194.
  • V. V. Uchaikin. Fractional derivatives for physicists and engineers.vol.1.Springer 2012.
  • W. Wyss. The fractional diffusion equation, J. Math. Phys., 27(11), (1986) 2782-2785.

Year 2017, Volume: 5 Issue: 3, 107 - 117, 01.07.2017

Arman Aghili

Abstract

References

  • A. Aghili, H. Zeinali. Advances in Laplace type integral transforms with applications. Indian Journal of Science and Technology, Vol 7(6), 877–890, June 2014.
  • A. Aghili, H. Zeinali. Solution to time fractional wave equation in the presence of friction via integral transform. Communications on applied nonlinear analysis, Vol.21, No.2, pp.67-88, 2014.
  • A. Aghili; M. R. Masomi. Integral transform method for solving different F.S.I.Es and P.F.D.Es. Konuralp Journal of Mathematics, Volume 2, No. 1 pp. 45-62, 2014.
  • T.M. Atanackovic , B.Stankovic. Dynamics of a visco -elastic rod of Fractional derivative type, Z. Angew. Math. Mech., 82(6), (2002) 377-386.
  • T. M. Atanackovic , B.Stankovic. On a system of differential equations with fractional derivatives arising in rod theory. Journal of Physics A: Mathematical and General, 37, No 4, 1241-1250 (2004).
  • D. G. Duffy. Transform methods for solving partial differential equations. Chapman and Hall/CRC, 2004.
  • R. S. Dahiya . M . Vinayagamoorthy.Laplace transfom pairs of n-dimensions and heat conduction problem. Math. Comput. Modelling vol. 13.No. 10 , pp,35-50.
  • V.A. Ditkin. A.P.Prudnikov. Operational calculus In two variables and its application ,Pergamon Press, New York,1962.
  • V. W. Ekman . On the influence of the earth’s rotation on ocean currents. Ark. Math. Astr. Fys. 2. No 1905.
  • A. A. Kilbass ,J. J. Trujillo. Differential equation of fractional order: methods, results and problems. II, Appl. Anal, 81(2), (2002)435-493.
  • Y. Luchko, H. M. Srivastava. The exact solution of certain differential equations of fractional Order by using operational calculus.Comput.Math.Appl.29 (1995)73-85.
  • S. Miller, B. Ross. An introduction to fractional differential equations,Wiley, NewYork.
  • K. B. Oldham, J. Spanier.The Fractional calculus,Academic Press, NewYork, 1974.
  • K. B. Oldham, J. Spanier, Fractional calculus and its applications, Bull.Inst.Politech.. Sect. I, 24 (28)(3-4), (1978) 29-34.
  • I. Podlubny, The Laplace transform method for linear differential equations of fractional order, Slovak Academy of sciences. Slovak Republic, 1994.
  • I. Podlubny. Fractional differential equations, Academic Press, San Diego, CA,1999.
  • G.E.Roberts, H. Kaufman. Table of Laplace transforms, Philadelphia; W.B.Saunders Co. 1966.
  • G. Samko , A. Kilbas. O. Marchiev. Fractional Integrals and derivatives theory and applications. Gordon and Breach,Amesterdam,1993.
  • W. Schneider, W. Wyss. Fractional diffusion and wave equations. J. Math. Phys.30(1989)134-144.
  • B.A.Stankovic. system of partial differential equations with fractional derivatives,Math. Vesnik, 3-4(54), (2002) 187-194.
  • V. V. Uchaikin. Fractional derivatives for physicists and engineers.vol.1.Springer 2012.
  • W. Wyss. The fractional diffusion equation, J. Math. Phys., 27(11), (1986) 2782-2785.
There are 22 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Arman Aghili

Publication Date July 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 3

Cite

APA Aghili, A. (2017). Non-homogenous KdV and coupled sub-ballistic fractional PDEs. New Trends in Mathematical Sciences, 5(3), 107-117.
AMA Aghili A. Non-homogenous KdV and coupled sub-ballistic fractional PDEs. New Trends in Mathematical Sciences. July 2017;5(3):107-117.
Chicago Aghili, Arman. “Non-Homogenous KdV and Coupled Sub-Ballistic Fractional PDEs”. New Trends in Mathematical Sciences 5, no. 3 (July 2017): 107-17.
EndNote Aghili A (July 1, 2017) Non-homogenous KdV and coupled sub-ballistic fractional PDEs. New Trends in Mathematical Sciences 5 3 107–117.
IEEE A. Aghili, “Non-homogenous KdV and coupled sub-ballistic fractional PDEs”, New Trends in Mathematical Sciences, vol. 5, no. 3, pp. 107–117, 2017.
ISNAD Aghili, Arman. “Non-Homogenous KdV and Coupled Sub-Ballistic Fractional PDEs”. New Trends in Mathematical Sciences 5/3 (July 2017), 107-117.
JAMA Aghili A. Non-homogenous KdV and coupled sub-ballistic fractional PDEs. New Trends in Mathematical Sciences. 2017;5:107–117.
MLA Aghili, Arman. “Non-Homogenous KdV and Coupled Sub-Ballistic Fractional PDEs”. New Trends in Mathematical Sciences, vol. 5, no. 3, 2017, pp. 107-1.
Vancouver Aghili A. Non-homogenous KdV and coupled sub-ballistic fractional PDEs. New Trends in Mathematical Sciences. 2017;5(3):107-1.
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