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Advisor(s)
Abstract(s)
The operational matrices of left Caputo fractional derivative, right Caputo
fractional derivative, and Riemann–Liouville fractional integral, for shiftedChebyshev
polynomials, are presented and derived.We propose an accurate and efficient spectral
algorithm for the numerical solution of the two-sided space–time Caputo fractionalorder
telegraph equation with three types of non-homogeneous boundary conditions,
namely, Dirichlet, Robin, and non-local conditions. The proposed algorithm is based
on shifted Chebyshev tau technique combined with the derived shifted Chebyshev
operational matrices.We focus primarily on implementing the novel algorithm both in
temporal and spatial discretizations. This algorithm reduces the problem to a system of
algebraic equations greatly simplifying the problem. This system can be solved by any
standard iteration method. For confirming the efficiency and accuracy of the proposed
scheme, we introduce some numerical examples with their approximate solutions and
compare our results with those achieved using other methods.
Description
Keywords
Fractional telegraph equation Fractional Klein–Gordon equation Operational matrix Shifted Chebyshev Tau method Riesz fractional derivative
Citation
Publisher
Springer Verlag