Variable order and distributed order fractional operators. (English) Zbl 1018.93007

Many physical processes appear to exhibit fractional order behaviour that may vary with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. The paper develops the concept of variable and distributed order fractional operators. The concept of distributed order operators in which the order of the time based operator depends on an additional independent spatial variable is also extended. Finally, operators of multivariable and distributed order are defined and their various applications outlined.


93B28 Operator-theoretic methods
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