2021, Vol. 2, Issue 1, Part A
Fractional differential equations: Change of variables and nonlocal symmetries
Author(s): Rano Sabirova
Abstract: The paper considers point changes of variables in integrals and fractional derivatives of various types. In the general case, such changes lead to the appearance of operators of fractional integro-differentiation of a function with respect to another function. The problem of extending the action of a group of point transformations to a given type of operators is solved, and the corresponding formulas for the continuation of the infinitesimal operator of the group are presented and proved. Using a simple example of an ordinary differential equation with a fractional derivative, we illustrate the application of continuation formulas to find some of its nonlocal symmetries and check them admitted by the equation.
Pages: 44-59 | Views: 674 | Downloads: 295
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How to cite this article:
Rano Sabirova. Fractional differential equations: Change of variables and nonlocal symmetries. Journal of Mathematical Problems, Equations and Statistics. 2021; 2(1): 44-59.