Research Article

Fixed point approach to Basset problem

Volume: 5 Number: 3 July 1, 2017
EN

Fixed point approach to Basset problem

Abstract

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.

Keywords

References

  1. Podlubny I: Mathematics in Science and Engineering 198. In Fractional Differential Equations. Academic Press, San Diego; 1999.
  2. Samko SG, Kilbas AA, Marichev OI: Fractional Integrals and Derivatives. Gordon & Breach, Yverdon; 1993.
  3. Basset AB: On the descent of a sphere in a viscous liquid. Q. J. Math. 1910, 42: 369-381.
  4. 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
  5. Ashyralyev A, Well-posedness of fractional parabolic equations, Boundary Value Problems, 2013: 2013:31, 1-18.
  6. 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.
  7. Petras I: Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer, New York (2011)
  8. Cakir Z: Stability of difference schemes for fractional parabolic PDE with the Dirichlet-Neumann conditions. Abstr. Appl. Anal. 2012., 2012: Article ID 463746

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Lale Cona *
Türkiye

Publication Date

July 1, 2017

Submission Date

January 31, 2017

Acceptance Date

February 7, 2017

Published in Issue

Year 2017 Volume: 5 Number: 3

APA
Cona, L. (2017). Fixed point approach to Basset problem. New Trends in Mathematical Sciences, 5(3), 175-181. https://izlik.org/JA52JE75UN
AMA
1.Cona L. Fixed point approach to Basset problem. New Trends in Mathematical Sciences. 2017;5(3):175-181. https://izlik.org/JA52JE75UN
Chicago
Cona, Lale. 2017. “Fixed Point Approach to Basset Problem”. New Trends in Mathematical Sciences 5 (3): 175-81. https://izlik.org/JA52JE75UN.
EndNote
Cona L (July 1, 2017) Fixed point approach to Basset problem. New Trends in Mathematical Sciences 5 3 175–181.
IEEE
[1]L. Cona, “Fixed point approach to Basset problem”, New Trends in Mathematical Sciences, vol. 5, no. 3, pp. 175–181, July 2017, [Online]. Available: https://izlik.org/JA52JE75UN
ISNAD
Cona, Lale. “Fixed Point Approach to Basset Problem”. New Trends in Mathematical Sciences 5/3 (July 1, 2017): 175-181. https://izlik.org/JA52JE75UN.
JAMA
1.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, vol. 5, no. 3, July 2017, pp. 175-81, https://izlik.org/JA52JE75UN.
Vancouver
1.Lale Cona. Fixed point approach to Basset problem. New Trends in Mathematical Sciences [Internet]. 2017 Jul. 1;5(3):175-81. Available from: https://izlik.org/JA52JE75UN