Journal
MATHEMATICS
Volume 8, Issue 3, Pages -Publisher
MDPI
DOI: 10.3390/math8030324
Keywords
fractional differential equations; numerical methods; smoothness assumptions; persistent memory
Categories
Funding
- COST (European Cooperation in Science and Technology) [CA15225]
- GNCS-INdAM 2019 Project
- German Federal Ministry of Education and Research (BMBF) [01IS17096A]
- National Natural Science Foundation of China [NSAF U1930402]
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The solution of fractional-order differential problems requires in the majority of cases the use of some computational approach. In general, the numerical treatment of fractional differential equations is much more difficult than in the integer-order case, and very often non-specialist researchers are unaware of the specific difficulties. As a consequence, numerical methods are often applied in an incorrect way or unreliable methods are devised and proposed in the literature. In this paper we try to identify some common pitfalls in the use of numerical methods in fractional calculus, to explain their nature and to list some good practices that should be followed in order to obtain correct results.
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