## THERMAL SCIENCE

International Scientific Journal

### FRACTIONAL VARIATIONAL ITERATION METHOD FOR TIME-FRACTIONAL NON-LINEAR FUNCTIONAL PARTIAL DIFFERENTIAL EQUATION HAVING PROPORTIONAL DELAYS

**ABSTRACT**

In this paper, time-fractional non-linear partial differential equation with proportional delays are solved by fractional variational iteration method taking into account modified Riemann-Liouville fractional derivative. The numerical solutions which are calculated by using this method are better than those obtained by homotopy perturbation method and differential transform method with same data set and approximation order. On the other hand, to improve the solutions obtained by fractional variational iteration method, residual error function is used. With this additional process, the resulting approximate solutions are getting closer to the exact solutions. The results obtained by taking into account different values of variables in the domain are supported by compared tables and graphics in detail.

**KEYWORDS**

PAPER SUBMITTED: 2017-06-12

PAPER REVISED: 2017-11-04

PAPER ACCEPTED: 2017-11-18

PUBLISHED ONLINE: 2018-01-07

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**Supplement 1**, PAGES [S33 - S46]

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