Abstract
We use the generalized L1 approximation for the Caputo fractional derivative, the second‐order fractional quadrature rule approximation for the integral term, and a classical Crank‐Nicolson alternating direction implicit (ADI) scheme for the time discretization of a new two‐dimensional (2D) fractional integro‐differential equation, in combination with a space discretization by an arbitrary‐order orthogonal spline collocation (OSC) method. The stability of a Crank‐Nicolson ADI OSC scheme is rigourously established, and error estimate is also derived. Finally, some numerical tests are given.
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