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Space-Fractional Transport Equation

Year 2020, Volume: 8 Issue: 2, 304 - 312, 27.10.2020

Abstract

In this article, the author consider certain space fractional equations using integral transforms and exponential operators. 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 exponential operators method is very convenient and effective. Constructive examples occur throughout the paper.                                                                    

Supporting Institution

University of Guilan

References

  • [1] A. Aghili, Solution to time fractional non homogeneous first order PDE with non constant coefficients.Tbilisi Mathematical Journal 12(4) (2019), pp. 149–155.
  • [2] A. Aghili, Fractional Black-Scholes equation, International Journal of Financial Engineering, 4(1)(2017) World Scientific Publishing Company, DOI:10.1142/S2424786317500049
  • [3] A. Aghili, Complete Solution For The Time Fractional Diffusion Problem With Mixed Boundary Conditions By Operational Method, Applied Mathematics and Non- linear Sciences, April (2020) (aop) 1-12.
  • [4] A. Aghili, Special functions, integral transforms with applications, Tbilisi Mathematical Journal 12 (1) (2019), 33-44.
  • [5] 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.
  • [6] A. Apelblat,Laplace transforms and their applications, Nova science publishers, Inc, New York, 2012.
  • [7] T.M. Atanackovic and B. Stankovic,Dynamics of a visco -elastic rod of Fractional derivative type, Z. Angew. Math. Mech., 82(6), (2002) 377-386.
  • [8] T.M. Atanackovic and 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).
  • [9] G. Dattoli, P.L. Ottaviani, A. Torre and L. Vazquez,Evolution operator equations: integrationwith algebraic and finite difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory, Riv. Nuovo Cimento 2 (1997) 1-133.
  • [10] W. Deng, Finite element method for the space and time fractional Fokker-Planck equation, SIAM J. Numer. Anal. 47 (2008) 204–226.
  • [11] D.G. Duffy, Transform methods for solving partial differential equations, Chapman and Hall/CRC, 2004.
  • [12] H. J. Glaeske, A.P.Prudnikov and K. A. Skornik, Operational Calculus And Related Topics, Chapman and Hall / CRC 2006.
  • [13] A. A. Kilbass and J.J. Trujillo, Differential equation of fractional order: methods, results and problems II, Appl. Anal, 81(2), (2002) 435-493. [14] K.B. Oldham and J. Spanier, The Fractional calculus, Academic Press, NewYork, 1974.
  • [15] K.B. Oldham and J. Spanier, Fractional calculus and its applications, Bull.Inst.Politech.. Sect. I, 24 (28)(3-4), (1978) 29-34. [16] I. Podlubny, Fractional differential equations, Academic Press, San Diego, CA,1999.
  • [17] I.N. Sneddon, Elements of partial differential equations, McGRAW-HILL International editions.21st. Printing 1988.
  • [18] W. Schneider and W. Wyss, Fractional diffusion and wave equations, J. Math. Phys.30(1989)134-144.
  • [19] F. Usta, H. Budak and M.Z. Sarıkaya,Yang-Laplace transform method Volterra and Abel’s integro-differential equations of fractional order, Int. J. Nonlinear Anal. Appl. 9 (2018) No. 2, 203-214.
  • [20] F. Usta, Fractional type Poisson equations by radial basis functions Kansa approach, Journal of Inequalities and Special Functions.Volume 7 Issue 4(2016), Pages 143-149.
  • [21] F. Usta, A conformable calculus of radial basis functions and its applications,An International Journal of Optimization and Control, Theories and Applications. Vol.8, No.2, pp.176-182 (2018)
  • [22] F. Usta,A mesh-free technique of numerical solution of newly defined conformable differential equations, Konuralp Journal of Mathematics.Volume 4 No. 2 pp. 149–157 (2016).
Year 2020, Volume: 8 Issue: 2, 304 - 312, 27.10.2020

Abstract

References

  • [1] A. Aghili, Solution to time fractional non homogeneous first order PDE with non constant coefficients.Tbilisi Mathematical Journal 12(4) (2019), pp. 149–155.
  • [2] A. Aghili, Fractional Black-Scholes equation, International Journal of Financial Engineering, 4(1)(2017) World Scientific Publishing Company, DOI:10.1142/S2424786317500049
  • [3] A. Aghili, Complete Solution For The Time Fractional Diffusion Problem With Mixed Boundary Conditions By Operational Method, Applied Mathematics and Non- linear Sciences, April (2020) (aop) 1-12.
  • [4] A. Aghili, Special functions, integral transforms with applications, Tbilisi Mathematical Journal 12 (1) (2019), 33-44.
  • [5] 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.
  • [6] A. Apelblat,Laplace transforms and their applications, Nova science publishers, Inc, New York, 2012.
  • [7] T.M. Atanackovic and B. Stankovic,Dynamics of a visco -elastic rod of Fractional derivative type, Z. Angew. Math. Mech., 82(6), (2002) 377-386.
  • [8] T.M. Atanackovic and 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).
  • [9] G. Dattoli, P.L. Ottaviani, A. Torre and L. Vazquez,Evolution operator equations: integrationwith algebraic and finite difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory, Riv. Nuovo Cimento 2 (1997) 1-133.
  • [10] W. Deng, Finite element method for the space and time fractional Fokker-Planck equation, SIAM J. Numer. Anal. 47 (2008) 204–226.
  • [11] D.G. Duffy, Transform methods for solving partial differential equations, Chapman and Hall/CRC, 2004.
  • [12] H. J. Glaeske, A.P.Prudnikov and K. A. Skornik, Operational Calculus And Related Topics, Chapman and Hall / CRC 2006.
  • [13] A. A. Kilbass and J.J. Trujillo, Differential equation of fractional order: methods, results and problems II, Appl. Anal, 81(2), (2002) 435-493. [14] K.B. Oldham and J. Spanier, The Fractional calculus, Academic Press, NewYork, 1974.
  • [15] K.B. Oldham and J. Spanier, Fractional calculus and its applications, Bull.Inst.Politech.. Sect. I, 24 (28)(3-4), (1978) 29-34. [16] I. Podlubny, Fractional differential equations, Academic Press, San Diego, CA,1999.
  • [17] I.N. Sneddon, Elements of partial differential equations, McGRAW-HILL International editions.21st. Printing 1988.
  • [18] W. Schneider and W. Wyss, Fractional diffusion and wave equations, J. Math. Phys.30(1989)134-144.
  • [19] F. Usta, H. Budak and M.Z. Sarıkaya,Yang-Laplace transform method Volterra and Abel’s integro-differential equations of fractional order, Int. J. Nonlinear Anal. Appl. 9 (2018) No. 2, 203-214.
  • [20] F. Usta, Fractional type Poisson equations by radial basis functions Kansa approach, Journal of Inequalities and Special Functions.Volume 7 Issue 4(2016), Pages 143-149.
  • [21] F. Usta, A conformable calculus of radial basis functions and its applications,An International Journal of Optimization and Control, Theories and Applications. Vol.8, No.2, pp.176-182 (2018)
  • [22] F. Usta,A mesh-free technique of numerical solution of newly defined conformable differential equations, Konuralp Journal of Mathematics.Volume 4 No. 2 pp. 149–157 (2016).
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Arman Aghili

Publication Date October 27, 2020
Submission Date January 14, 2020
Acceptance Date July 13, 2020
Published in Issue Year 2020 Volume: 8 Issue: 2

Cite

APA Aghili, A. (2020). Space-Fractional Transport Equation. Konuralp Journal of Mathematics, 8(2), 304-312.
AMA Aghili A. Space-Fractional Transport Equation. Konuralp J. Math. October 2020;8(2):304-312.
Chicago Aghili, Arman. “Space-Fractional Transport Equation”. Konuralp Journal of Mathematics 8, no. 2 (October 2020): 304-12.
EndNote Aghili A (October 1, 2020) Space-Fractional Transport Equation. Konuralp Journal of Mathematics 8 2 304–312.
IEEE A. Aghili, “Space-Fractional Transport Equation”, Konuralp J. Math., vol. 8, no. 2, pp. 304–312, 2020.
ISNAD Aghili, Arman. “Space-Fractional Transport Equation”. Konuralp Journal of Mathematics 8/2 (October 2020), 304-312.
JAMA Aghili A. Space-Fractional Transport Equation. Konuralp J. Math. 2020;8:304–312.
MLA Aghili, Arman. “Space-Fractional Transport Equation”. Konuralp Journal of Mathematics, vol. 8, no. 2, 2020, pp. 304-12.
Vancouver Aghili A. Space-Fractional Transport Equation. Konuralp J. Math. 2020;8(2):304-12.
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