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Basic Theory (De Gruyter Reference)

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Basic Theory (De Gruyter Reference), 9783110570816 (3110570815), De Gruyter, 2019
Fractional calculus (FC) originated in 1695, nearly at the same time as conventional calculus. However, FC attracted limited attention and remained a pure mathematical exercise, in spite of the contributions of important mathematicians, physicists and engineers. FC had a rapid development during the last few decades, both in mathematics and in the applied sciences, it being nowadays recognized as an excellent tool fordescribingcomplexsystems,phenomenainvolvinglongrangememoryeffectsand non-locality.Ahugenumberofresearchpapersandbooksdevotedtothissubjecthave beenpublished,andpresentlyseveralspecializedconferencesandworkshopsarebeing organized each year. The FC popularity in all fields of science is due to its successful application in mathematical models, namely in the form of FC operators and fractional integral and differential equations. Presently, we are witnessing considerable progress both as regards theoretical aspects and applications of FC in areas such as physics, engineering, biology, medicine, economy, or finance.

The popularity of FC has attracted many researchers from all over the world and there is a demand for works covering all areas of science in a systematic and rigorous form. In fact, the literature devoted to FC and its applications is huge, but readers are confronted with a high heterogeneity and, in some cases, with misleading and inaccurate information. The Handbook of Fractional Calculus with Applications (HFCA) intends to fill that gap and provides the readers with a solid and systematic treatment of the main aspects and applications of FC. Motivated by these ideas, the editors of the volumes involved a team of internationally recognized experts for a joint publishing project offering a survey of their own and other important results in their fields of research. As a result of these joint efforts, a modern survey of FC and its applications, reflectingpresentdayscientificknowledge,isnowavailablewiththeHFCA.Thiswork is distributed in the form of several distinct volumes, each one developed under the supervision of its editors.
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