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- Title
Solutions of Initial Value Problems with Non-Singular, Caputo Type and Riemann-Liouville Type, Integro-Differential Operators.
- Authors
Angstmann, Christopher N.; Burney, Stuart-James M.; Henry, Bruce I.; Jacobs, Byron A.
- Abstract
Motivated by the recent interest in generalized fractional order operators and their applications, we consider some classes of integro-differential initial value problems based on derivatives of the Riemann–Liouville and Caputo form, but with non-singular kernels. We show that, in general, the solutions to these initial value problems possess discontinuities at the origin. We also show how these initial value problems can be re-formulated to provide solutions that are continuous at the origin but this imposes further constraints on the system. Consideration of the intrinsic discontinuities, or constraints, in these initial value problems is important if they are to be employed in mathematical modelling applications.
- Subjects
INITIAL value problems; INTEGRO-differential equations; FRACTIONAL calculus
- Publication
Fractal & Fractional, 2022, Vol 6, Issue 8, p436
- ISSN
2504-3110
- Publication type
Article
- DOI
10.3390/fractalfract6080436