### STABILITY AND ERROR OF THE NEW NUMERICAL SOLUTION OF FRACTIONAL RIESZ SPACE TELEGRAPH EQUATION WITH TIME DELAY

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#### Abstract

In this paper, we propose a numerical method for Riesz space fractional telegraph equation with time delay. The Riesz fractional telegraph equation is approximated with the interpolating polynomial P2. First a system of fractional differential equations are obtained from the telegraph equation with respect to the time variable. Then our numerical algorithm is proposed. The convergence order and stability of the fractional order algorithms are proved. Finally, some numerical examples are constructed to describe the usefulness and profitability of the numerical method. Numerical results show that the accuracy of order O(t3).

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DOI: https://doi.org/10.22190/FUMI210401012A

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