Abstract
In this work, we investigate the stability and the structural stability of a class of fractional boundary value problems. We approximate the solution by using a wide range of numerical methods illustrating our theoretical results.
Mathematics Subject Classification (2010). Primary 65L05; Secondary 34D10.
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References
M. Caputo, Elasticity e Dissipazione, Zanichelli, Bologna, 1969.
C. Corduneanu, Principles of Differential and Integral Equations. Allyn and Bacon, Boston, 1971.
K. Diethelm, An algorithm for the numerical solution of differential equations of fractional order Electr. Trans. Numer. Anal. 5 (1997), 1–6.
K. Diethelm and N.J. Ford, Analysis of fractional differential equations J. Math. Anal. Appl. 265 (2002), 229–248.
K. Diethelm, and N.J. Ford, Volterra integral equations and fractional calculus: Do neighbouring solutions intersect? Journal of Integral Equations and Applications, to appear.
K. Diethelm, N.J. Ford, and A.D. Freed, A predictor-corrector approach for the numerical solution of fractional differential equations Nonlinear Dynamics. 29 (2002), 3–22.
K. Diethelm, J.M. Ford, N.J. Ford and M. Weilbeer, Pitfalls in fast numerical solvers for fractional differential equations J. Comp. Appl. Mathem. 186 2 (2006), 482–503.
N.J. Ford and J.A. Connolly, Comparison of numerical methods for fractional differential equations Commun. Pure Appl. Anal. 5, no 2 (2006), 289–307.
N.J. Ford and M.L. Morgado, Structural Stability for Fractional Differential Equations as Boundary Value Problems AIP Conference Proceedings 1281, (2010), 1191– 1194, 8th ICNAAM 2010, 19–25 September, Rhodes, Greece.
N.J. Ford and M.L. Morgado, Fract. Calc. Appl. Anal., Vol. 14, No 4 (2011), pp. 554–567; DOI: 10.2478/s13540-011-0034-4.
E. Hairer, Ch. Lubich and M. Schlichte, Fast numerical solution of weakly singular Volterra integral equations J. Comp. Appl. Mathem. 23 (1988), 87–98.
S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Yverdon, 1993.
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Ford, N.J., Morgado, M.L. (2013). Stability, Structural Stability and Numerical Methods for Fractional Boundary Value Problems. In: Almeida, A., Castro, L., Speck, FO. (eds) Advances in Harmonic Analysis and Operator Theory. Operator Theory: Advances and Applications, vol 229. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0516-2_9
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DOI: https://doi.org/10.1007/978-3-0348-0516-2_9
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