## THERMAL SCIENCE

International Scientific Journal

### EXACT SOLUTIONS OF TIME FRACTIONAL HEAT-LIKE AND WAVE-LIKE EQUATIONS WITH VARIABLE COEFFICIENTS

**ABSTRACT**

In this paper, a variable-coefficient time fractional heat-like and wave-like equation with initial and boundary conditions is solved by the use of variable separation method and the properties of Mittag-Leffler function. As a result, exact solutions are obtained, from which some known special solutions are recovered. It is shown that the variable separation method can also be used to solve some others time fractional heat-like and wave-like equation in science and engineering.

**KEYWORDS**

PAPER SUBMITTED: 2015-11-12

PAPER REVISED: 2016-02-01

PAPER ACCEPTED: 2016-02-18

PUBLISHED ONLINE: 2016-09-24

**THERMAL SCIENCE** YEAR

**2016**, VOLUME

**20**, ISSUE

**Supplement 3**, PAGES [S689 - S693]

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