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Space-Fractional Transport Equation

Yıl 2020, Cilt: 8 Sayı: 2, 304 - 312, 27.10.2020

Öz

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.                                                                    

Destekleyen Kurum

University of Guilan

Kaynakça

  • [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).
Yıl 2020, Cilt: 8 Sayı: 2, 304 - 312, 27.10.2020

Öz

Kaynakça

  • [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).
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Arman Aghili

Yayımlanma Tarihi 27 Ekim 2020
Gönderilme Tarihi 14 Ocak 2020
Kabul Tarihi 13 Temmuz 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 2

Kaynak Göster

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. Ekim 2020;8(2):304-312.
Chicago Aghili, Arman. “Space-Fractional Transport Equation”. Konuralp Journal of Mathematics 8, sy. 2 (Ekim 2020): 304-12.
EndNote Aghili A (01 Ekim 2020) Space-Fractional Transport Equation. Konuralp Journal of Mathematics 8 2 304–312.
IEEE A. Aghili, “Space-Fractional Transport Equation”, Konuralp J. Math., c. 8, sy. 2, ss. 304–312, 2020.
ISNAD Aghili, Arman. “Space-Fractional Transport Equation”. Konuralp Journal of Mathematics 8/2 (Ekim 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, c. 8, sy. 2, 2020, ss. 304-12.
Vancouver Aghili A. Space-Fractional Transport Equation. Konuralp J. Math. 2020;8(2):304-12.
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