A Computational Approach for the Solution of A Class of Variable-Order Fractional Integro-Differential Equations With Weakly Singular Kernels

A Computational Approach for the Solution of A Class of Variable-Order Fractional Integro-Differential Equations With Weakly Singular Kernels

A new computational approach for approximating of variable-order fractional derivatives is proposed. The technique is based on piecewise cubic spline interpolation. The method is extended to a class of nonlinear variable-order fractional integro-differential equation with weakly singular kernels. Il...

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Veröffentlicht in:Fractional calculus & applied analysis 2017-08, Vol.20 (4), p.1023-1042
Hauptverfasser: Moghaddam, Behrouz Parsa, Tenreiro Machado, José António
Format: Artikel
Sprache:eng
Schlagworte:
41A15
45G05
45J05
65C20
65L12
Abstract Harmonic Analysis
Analysis
Computation
convergence order
Differential equations
finite difference approximation
Functional Analysis
Integral Transforms
Kernels
Mathematical analysis
Mathematics
Operational Calculus
Primary 26A33
Research Paper
Secondary 33F05
spline approximation
variable-order fractional calculus
weakly singular integro-differential equation
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Beschreibung
Zusammenfassung:A new computational approach for approximating of variable-order fractional derivatives is proposed. The technique is based on piecewise cubic spline interpolation. The method is extended to a class of nonlinear variable-order fractional integro-differential equation with weakly singular kernels. Illustrative examples are discussed, demonstrating the performance of the numerical scheme.
ISSN:1311-0454
1314-2224
DOI:10.1515/fca-2017-0053