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Non-additivity and additivity in general fractional calculus and its physical interpretationsстатья Исследовательская статья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Автор: Tarasov V.E.
- Журнал: Fractal and Fractional
- Том: 8
- Номер: 9
- Год издания: 2024
- Издательство: MDPI Publishing
- Местоположение издательства: Basel, Switzerland, Switzerland
- Первая страница: 535-1
- Последняя страница: 535
- Номер статьи: 535-36
- DOI: 10.3390/fractalfract8090535
- Аннотация: In this work, some properties of the general convolutional operators of general fractionalcalculus (GFC), which satisfy analogues of the fundamental theorems of calculus, are described. Twotypes of general fractional (GF) operators on a finite interval exist in GFC that are conventionallycalled the L-type and T-type operators. The main difference between these operators is that theadditivity property holds for T-type operators and is violated for L-type operators. This property isvery important for the application of GFC in physics and other sciences. The presence or violationof the additivity property can be associated with qualitative differences in the behavior of physicalprocesses and systems. In this paper, we define L-type line GF integrals and L-type line GF gradients.For these L-type operators, the gradient theorem is proved in this paper. In general, the L-type lineGF integral over a simple line is not equal to the sum of the L-type line GF integrals over lines thatmake up the entire line. In this work, it is shown that there exist two cases when the additivityproperty holds for the L-type line GF integrals. In the first case, the L-type line GF integral along theline is equal to the sum of the L-type line GF integrals along parts of this line only if the processes, which are described by these lines, are independent. Processes are called independent if the history of changes in the subsequent process does not depend on the history of the previous process. In thesecond case, we prove the additivity property holds for the L-type line GF integrals, if the conditionsof the GF gradient theorems are satisfied.
- Добавил в систему: Тарасов Василий Евгеньевич