On the stability estimates and numerical solution of fractional order telegraph integro-differential equation

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Abstract
We consider an initial-boundary value problem for fractional order telegraph integro-differential equation. In this study, fractional derivative can be considered in both Riemann-Liouville and Caputo senses since our initial condition is zero. We calculate approximate numerical solutions by constructing first and second order finite difference schemes. Estimations of the stability of finite difference scheme is given and also for some fractional orders, numerical examples are given to confirm the accuracy of the established difference scheme with respect to exact solution. Also some plots are presented for large values of x and t . Finally we show that our solutions continuously depend on the fractional derivatives by plotting error graph while increasing fractional order.

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