Handbook of Fractional Calculus with Applications: Applications in Engineering, Life and Social Sciences, Part A (De Gruyter Reference)

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. 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 This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This seventh volume collects authoritative chapters covering several applications of fractional calculus in in engineering, life, and social sciences, including applications in biology and medicine, mechanics of complex media, economy, and electrical devices.