Abstract
This work investigates several discretizations of the Erdélyi-Kober fractional operator and their use in integro-differential equations. We propose two methods of discretizing E-K operator and prove their errors asymptotic behaviour for several different variants of each discretization. We also determine the exact form of error constants. Next, we construct a finite-difference scheme based on a trapezoidal rule to solve a general first order integro-differential equation. As is known from the theory of Abel integral equations, the rate of convergence of any finite-different method depends on the severity of kernel’s singularity. We confirm these results in the E-K case and illustrate our considerations with numerical examples.
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Płociniczak, Ł., Sobieszek, S. Numerical schemes for integro-differential equations with Erdélyi-Kober fractional operator. Numer Algor 76, 125–150 (2017). https://doi.org/10.1007/s11075-016-0247-z
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DOI: https://doi.org/10.1007/s11075-016-0247-z