2016
DOI: 10.1515/fca-2016-0059
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Fractional Calculus: D’où Venons-Nous? Que Sommes-Nous? Où Allons-Nous?

Abstract: Discussions under this title, inspired by the famous Gauguin painting,

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Cited by 31 publications
(13 citation statements)
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“…The reason is that the differential and integral equations and dynamical systems of fractional order can model mathematically the phenomena of Nature and Society more adequately than these restricted to integer order. The evolution of FC was analyzed in several survey papers and round tables discussions [103,104,105,101,102,107,108] revealing a considerable and sustained progress. Therefore, it is important to collect the most recent information not only to keep a precise record, but also to monitor the present day development.…”
Section: Introductionmentioning
confidence: 99%
“…The reason is that the differential and integral equations and dynamical systems of fractional order can model mathematically the phenomena of Nature and Society more adequately than these restricted to integer order. The evolution of FC was analyzed in several survey papers and round tables discussions [103,104,105,101,102,107,108] revealing a considerable and sustained progress. Therefore, it is important to collect the most recent information not only to keep a precise record, but also to monitor the present day development.…”
Section: Introductionmentioning
confidence: 99%
“…generalising the causal expression (19) to real orders. For the anti-causal case, we get the general expression:…”
Section: Second Unificationmentioning
confidence: 99%
“…Several of these questions and others were discussed in round tables in the scope of several meetings held by the fractional calculus community [18,19]. Nevertheless, present day state of affairs reveals that they were not sufficient to stimulate all researchers for a systematic definition of the fundamental concepts.…”
Section: Introductionmentioning
confidence: 99%
“…Notwithstanding this development a singular situation exists, since there is no definition of "fractional definite integral" [5,6]. Even more strangely, it seems that no-one has the goal to propose such a adefinition [7,8]. In fact, the term FI is used for an indefinite integral, which, as we will see, stands for a primitivation operation.…”
Section: Introductionmentioning
confidence: 99%