General Non-Local Continuum Mechanics: Derivation of Balance Equations

Vasily E. Tarasov
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Vasily E. Tarasov: Faculty “Information Technologies and Applied Mathematics”, Moscow Aviation Institute (National Research University), 125993 Moscow, Russia

Mathematics, 2022, vol. 10, issue 9, 1-43

Abstract: In this paper, mechanics of continuum with general form of nonlocality in space and time is considered. Some basic concepts of nonlocal continuum mechanics are discussed. General fractional calculus (GFC) and general fractional vector calculus (GFVC) are used as mathematical tools for constructing mechanics of media with general form of nonlocality in space and time. Balance equations for mass, momentum, and energy, which describe conservation laws for nonlocal continuum, are derived by using the fundamental theorems of the GFC. The general balance equation in the integral form are derived by using the second fundamental theorems of the GFC. The first fundamental theorems of GFC and the proposed fractional analogue of the Titchmarsh theorem are used to derive the differential form of general balance equations from the integral form of balance equations. Using the general fractional vector calculus, the equations of conservation of mass, momentum, and energy are also suggested for a wide class of regions and surfaces.

Keywords: non-local mechanics; fractional dynamics; fractional calculus; prosesses with memory; general fractional calculus (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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