Fractional calculus (FC) originated in 1695, nearly at the same time as conventional
calculus. However, FC attracted limited attention and remained a purely mathemati-
cal exercise in spite of the original contributions of important mathematicians, physi-
cists, and engineers. FC underwent a rapid development during the last few decades,
both in mathematics and applied sciences, being nowadays recognized as an excel-
lent tool for describing complex systems and phenomena involving long-range mem-
ory e䭋ects and non-locality. A huge number of research papers and books devoted to
this subject have been published, and each year several specialized conferences and
workshops are organized. The popularity of FC in all 倀elds of science is due to its suc-
cessful application in mathematical models, namely, in the form of FC operators and
fractional integral and di䭋erential equations. Presently, we are witnessing consider-
able progress both in theoretical aspects and in applications of FC in areas such as
physics, engineering, biology, medicine, economy, and 倀nance.
Author(s): Dumitru Baleanu, António Mendes Lopes
Publisher: De Gruyter
Year: 2019
Language: English
Pages: 259
Cover
......Page 1
Handbook of
Fractional Calculus
with Applications, Volume 7: Applications in Engineering, Life and Social
Sciences, Part A
......Page 5
© 2019......Page 6
Preface......Page 7
Contents
......Page 9
1 Fractional differential equations
with bio-medical applications......Page 11
2 Fractional-order modeling of
electro-impedance spectroscopy information......Page 31
3 Numerical solutions of singular time-fractional
PDEs......Page 53
4 A multi-scale model of nociception pathways
and pain mechanisms......Page 65
5 Variable-order derivatives and bone
remodeling in the presence of metastases......Page 79
6 Skeletal muscle modeling by fractional
multi-models: analysis of length effect......Page 105
7 Fractional calculus for modeling unconfined
groundwater......Page 129
8 Fractional calculus models in dynamic
problems of viscoelasticity......Page 149
9 Fractional calculus in structural mechanics......Page 169
10 Anomalous solute transport in complex media......Page 203
11 Application of variable-order fractional
calculus in solid mechanics......Page 217
12 Fractional heat conduction models and
their applications......Page 235
Index......Page 257
Back Cover A......Page 259
