## THERMAL SCIENCE

International Scientific Journal

### FRACTIONAL DERIVATIVE OF INVERSE MATRIX AND ITS APPLICATIONS TO SOLITON THEORY

**ABSTRACT**

In this paper, a formula of the local fractional partial derivative of inverse matrix is presented and proved. With the help of the derived formula, two new non-linear PDE are derived including the local fractional non-isospectral self-dual Yang-Mills equation and the local fractional principal chiral field equation. It is shown that the formula of the local fractional partial derivative of inverse matrix can be used to derive some other local fractional non-linear PDE in soliton theory.

**KEYWORDS**

PAPER SUBMITTED: 2019-04-28

PAPER REVISED: 2019-08-29

PAPER ACCEPTED: 2019-08-29

PUBLISHED ONLINE: 2020-06-21

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**4**, PAGES [2597 - 2604]

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