An historical perspective on fractional calculus in linear viscoelasticity

By Francesco Mainardi. 2010

164 citations recorded by the source corpus.

The article provides an historical survey of the early contributions on the applications of fractional calculus in linear viscoelasticty. The period under examination covers four decades, since 1930’s up to 1970’s, and authors are from both Western and Eastern countries. References to more recent contributions may be found in the bibliography of the author’s book.This paper reproduces, with Publisher’s permission, Section 3.5 of the book: F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity, Imperial College Press-London and World Scienific-Singapore, 2010.

Subfields: Fluid Flow and Transfer Processes, Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/13085d5180f5bb993075b0586d4d19785c052325

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Fluid Flow and Transfer Processes

1. Virginia S. Kiryakova
2. J. Machado
3. Duarte Valério
4. Sergei Rogosin
5. Giorgio Spada
6. Francesco Mainardi
7. Xiao-jun Yang
8. C. Sin

In Mechanics of Materials

1. J. Machado
2. Sergei Rogosin
3. Virginia S. Kiryakova
4. Duarte Valério
5. Giorgio Spada
6. Francesco Mainardi
7. Rudolf Gorenflo
8. Om Prakash Agrawal

In Modeling and Simulation

1. Virginia S. Kiryakova
2. J. Machado
3. Sergei Rogosin
4. Duarte Valério
5. Francesco Mainardi
6. Giorgio Spada
7. Vasily E. Tarasov
8. Xiao-jun Yang

Citations in the corpus

• Creep, relaxation and viscosity properties for basic fractional models in rheology (2011, background): “ty (Newton fluid), see e.g. [35]. Scott–Blair was surely a pioneer of the fractional calculus even if he did not provide a mathematical theory accepted by mathematicians of his time, as pointed out in [28]. It is known that the creep and relaxation power laws of the Scott–Blair model can be interpret”
• Some pioneers of the applications of fractional calculus (2013, methodology): “This fractional transfer function, first published in a series of papers in 1941–1943, was the first viscoelastic relationship proposed, see [41].”
• The Role of the Mittag-Leffler Function in Fractional Modeling (2015, background): “Since then, several other authors have pointed out the relevance of the Mittag-Leffler function to fractional viscoelastic models (see [15,52–54] and the references therein).”