Title: A Critical Review of Fractional Operators With Nonsingular Kernels
Abstract: Over the recent years, the fractional calculus community has seen a substantial influx of newconcepts for fractional operators. A main part of this work has been devoted to operators withcontinuous kernels. The idea behind these developments has been the fact that the singular kernelspresent in classical fractional differential and integral operators (like Riemann-Liouville, Caputoetc.) imply the non-smoothness of the solutions to associated differential or integral equations,which (among others) leads to major challenges in the construction of rapidly convergent numerical solution methods. Inprinciple, such effects can be avoided if continuous kernels are used.Unfortunately, it is often overlooked that the use of operators with continuous kernels introducesmany new and often even more severe problems, for example the non-existence of solutions. In thistalk we critically review the properties of fractional operators with nonsingular kernels and providearguments why their use should be avoided.
Bio:
- 1992: Diploma in Mathematics, TU Braunschweig1992-1998: Scientific Assistant, Institute of Mathematics, University of Hildesheim
- (PhD in Computer Science 1994; Habilitation in Mathematics 1998)1998-2004: (Senior) Scientific Assistant, Department of Numerical Mathematics, TU Braunschweig
- (Adjunct Professor since 2002)1999-2000: Temporary Professor for Numerical Mathematics, University of Gießen2004-2018 Software developer and project coordinator, GNS Gesellschaft für numerische Simulation mbH, Braunschweigsince 2018: Professor for Mathematics and Applied Computer Science, Technical University of Applied Sciences Würzburg-SchweinfurtEditorial Board Member for
- Fract. Calc. Appl. Anal.
- Numer. Algorithms
- J. Sci. Comput.
- J. Integral Equations Appl.
- J. Comput. Appl. Math.
- Comput. Appl. Math.