Publication Cover
Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 10
258
Views
11
CrossRef citations to date
0
Altmetric
Articles

An extension of the well-posedness concept for fractional differential equations of Caputo’s type

Pages 2126-2135 | Received 16 Sep 2013, Accepted 01 Dec 2013, Published online: 10 Jan 2014

References

  • Diethelm K. The analysis of fractional differential equations. Berlin: Springer; 2010.
  • Diethelm K, Ford NJ. Analysis of fractional differential equations. J. Math. Anal. Appl. 2002;265:229–248.
  • Tisdell CC. On the application of sequential and fixed-point methods to fractional differential equations of arbitrary order. J. Int. Equ. Appl. 2012;24:283–319.
  • Caputo M. Linear models of dissipation whose Q is almost frequency independent – II. Geophys. J. Roy. Astron. Soc. 1967;13:529–539; reprinted in Fract. Calc. Appl. Anal. 2008;11:4–14.
  • Caputo M, Mainardi F. A new dissipation model based on memory mechanism. Pure Appl. Geophys. 1971;91:134–147; reprinted in Fract. Calc. Appl. Anal. 2007;10:310–323.
  • Evangelatos GI, Spanos PD. An accelerated Newmark scheme for integrating the equation of motion of nonlinear systems comprising restoring elements governed by fractional derivatives. In: Gdoutos M, editor. Recent advances in mechanics. New York (NY): Springer; 2011. p. 159–177.
  • Diethelm K. A fractional calculus based model for the simulation of an outbreak of dengue fever. Nonlinear Dyn. 2013;71:613–619.
  • Benson DA, Schumer R, Meerschaert MM, Wheatcraft SW. Fractional dispersion, Lévy motion, and the MADE tracer tests. Transp. Porous Media. 2001;42:211–240.
  • Meerschaert MM. Fractional calculus, anomalous diffusion, and probability. In: Klafter J, Lim SC, Metzler R, editors. Fractional dynamics. Singapore: World Scientific; 2011. p. 265–284.
  • Diethelm K. On the separation of solutions of fractional differential equations. Fract. Calc. Appl. Anal. 2008;11:259–268.
  • Diethelm K, Ford NJ. Volterra integral equations and fractional calculus: do neighboring solutions intersect? J. Int. Equ. Appl. 2012;24:25–37.
  • Ford NJ, Morgado ML. Stability, structural stability and numerical methods for fractional boundary value problems. Oper. Theory Adv. Appl. 2013;229:157–173.
  • Mureşan V. A Gronwall type inequality for Fredholm operators. Mathematica. 1999;41:227–231.
  • Linz P. Analytical and numerical methods for Volterra equations. Philadelphia: SIAM; 1985.
  • Ford NJ, Morgado ML, Rebelo M. High order numerical methods for fractional terminal value problems. Comput. Meth. Appl. Math. Forthcoming. doi:10.1515/cmam-2013-022.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.