Rothe time discretization method for fractional integro-differential equations

Abstract

We consider an initial boundary value problem for a fractional order partial integro-differential equation. This problem is reformulated as an abstract fractional order integro-differential equation in a Banach space. We apply Rothe’s method of time discretization to establish the existence and uniqueness of a strong solution of the abstract problem which in turn guarantees the well-posedness of the initial boundary value problem. Rothe’s method has an orientation towards numerical methods as it established a priori estimates on the approximate solution.

Keywords:

• Rothe’s method
• Riemann–Liouville fractional derivative
• strong solution
• m-accretive operator

Acknowledgments

The author would like to thank the referees for their valuable comments/suggestions for improving the original manuscript.