Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2017, Cilt: 5 Sayı: 3, 175 - 181, 01.07.2017

Öz

Kaynakça

  • Podlubny I: Mathematics in Science and Engineering 198. In Fractional Differential Equations. Academic Press, San Diego; 1999.
  • Samko SG, Kilbas AA, Marichev OI: Fractional Integrals and Derivatives. Gordon & Breach, Yverdon; 1993.
  • Basset AB: On the descent of a sphere in a viscous liquid. Q. J. Math. 1910, 42: 369-381.
  • Ashyralyev A: Well-posedness of the Basset problem in spaces of smooth functions. Appl. Math. Lett. 2011, 24: 1176-1180. 10.1016/j.aml.2011.02.002
  • Ashyralyev A, Well-posedness of fractional parabolic equations, Boundary Value Problems, 2013: 2013:31, 1-18.
  • Baleanu D, Garra, R, Petras, I: A Fractional Variational Approach to the Fractional Basset-Type Equation, Reports on Mathematical Physics, 72 (1) 57-64, 2013.
  • Petras I: Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer, New York (2011)
  • Cakir Z: Stability of difference schemes for fractional parabolic PDE with the Dirichlet-Neumann conditions. Abstr. Appl. Anal. 2012., 2012: Article ID 463746
  • Ashyralyev A, Cakir Z: On the numerical solution of fractional parabolic partial differential equations with the Dirichlet condition. Discrete Dyn. Nat. Soc. 2012., 2012: Article ID 696179.
  • Ashyralyev A. , Z. Cakir; FDMfor fractional parabolic equations with the Neumann condition, Advances in Difference Equations, Vol. 2013, No. 120, doi:10.1186/1687-1847-2013-120, 2013.
  • Ashyralyev A., A note on fractional derivatives and fractional powers of operators. JMAA, 357(2009) 232-236.
  • Ashyralyev A., N. Emirov, Z. Cakir; Well-posedness of fractional parabolic differential and difference equations with Dirchlet-Neumann condition, Electronic Journal of Differential Equations, Vol. 2014, No. 97, pp. 1—17, 2014.
  • Erwin Kreyszig, Advanced Engineering Mathematics, John Willey & Sons, New York,1993.

Fixed point approach to Basset problem

Yıl 2017, Cilt: 5 Sayı: 3, 175 - 181, 01.07.2017

Öz

In the present paper, a sufficient condition for existence and uniqueness of Basset problem is obtained. The theorem on existence and uniqueness is established. This approach permits us to use fixed point iteration method to solve problem for differential equation involving derivatives of nonlinear order.

Kaynakça

  • Podlubny I: Mathematics in Science and Engineering 198. In Fractional Differential Equations. Academic Press, San Diego; 1999.
  • Samko SG, Kilbas AA, Marichev OI: Fractional Integrals and Derivatives. Gordon & Breach, Yverdon; 1993.
  • Basset AB: On the descent of a sphere in a viscous liquid. Q. J. Math. 1910, 42: 369-381.
  • Ashyralyev A: Well-posedness of the Basset problem in spaces of smooth functions. Appl. Math. Lett. 2011, 24: 1176-1180. 10.1016/j.aml.2011.02.002
  • Ashyralyev A, Well-posedness of fractional parabolic equations, Boundary Value Problems, 2013: 2013:31, 1-18.
  • Baleanu D, Garra, R, Petras, I: A Fractional Variational Approach to the Fractional Basset-Type Equation, Reports on Mathematical Physics, 72 (1) 57-64, 2013.
  • Petras I: Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer, New York (2011)
  • Cakir Z: Stability of difference schemes for fractional parabolic PDE with the Dirichlet-Neumann conditions. Abstr. Appl. Anal. 2012., 2012: Article ID 463746
  • Ashyralyev A, Cakir Z: On the numerical solution of fractional parabolic partial differential equations with the Dirichlet condition. Discrete Dyn. Nat. Soc. 2012., 2012: Article ID 696179.
  • Ashyralyev A. , Z. Cakir; FDMfor fractional parabolic equations with the Neumann condition, Advances in Difference Equations, Vol. 2013, No. 120, doi:10.1186/1687-1847-2013-120, 2013.
  • Ashyralyev A., A note on fractional derivatives and fractional powers of operators. JMAA, 357(2009) 232-236.
  • Ashyralyev A., N. Emirov, Z. Cakir; Well-posedness of fractional parabolic differential and difference equations with Dirchlet-Neumann condition, Electronic Journal of Differential Equations, Vol. 2014, No. 97, pp. 1—17, 2014.
  • Erwin Kreyszig, Advanced Engineering Mathematics, John Willey & Sons, New York,1993.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Lale Cona

Yayımlanma Tarihi 1 Temmuz 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 3

Kaynak Göster

APA Cona, L. (2017). Fixed point approach to Basset problem. New Trends in Mathematical Sciences, 5(3), 175-181.
AMA Cona L. Fixed point approach to Basset problem. New Trends in Mathematical Sciences. Temmuz 2017;5(3):175-181.
Chicago Cona, Lale. “Fixed Point Approach to Basset Problem”. New Trends in Mathematical Sciences 5, sy. 3 (Temmuz 2017): 175-81.
EndNote Cona L (01 Temmuz 2017) Fixed point approach to Basset problem. New Trends in Mathematical Sciences 5 3 175–181.
IEEE L. Cona, “Fixed point approach to Basset problem”, New Trends in Mathematical Sciences, c. 5, sy. 3, ss. 175–181, 2017.
ISNAD Cona, Lale. “Fixed Point Approach to Basset Problem”. New Trends in Mathematical Sciences 5/3 (Temmuz 2017), 175-181.
JAMA Cona L. Fixed point approach to Basset problem. New Trends in Mathematical Sciences. 2017;5:175–181.
MLA Cona, Lale. “Fixed Point Approach to Basset Problem”. New Trends in Mathematical Sciences, c. 5, sy. 3, 2017, ss. 175-81.
Vancouver Cona L. Fixed point approach to Basset problem. New Trends in Mathematical Sciences. 2017;5(3):175-81.