The Unified Theory of Shifted Convolution Quadrature for Fractional Calculus

This work devotes to developing a systematic and convenient approach based on the celebrated convolution quadrature theory design analyze difference formulas for fractional calculus at an arbitrary shifted point $$x_{n-\theta }$$ . The developed theory, called (SCQ), covers most from aspects of characterizing formation related generating functions which are convergent with integer orders. For stability reasons, theoretical determination parameter $$\theta $$ is provided fill gap in choice depends heavily experiments particularly non-integer order derivatives. Further, discuss effects A( $$\delta )-stability, regions several generalized popular within SCQ examined crucial robust numerical schemes. Some tests also considered demonstrate necessity introducing practical purposes.