## THERMAL SCIENCE

International Scientific Journal

### A NEW GENERAL FRACTIONAL DERIVATIVE GOLDSTEIN-KAC-TYPE TELEGRAPH EQUATION

**ABSTRACT**

In this paper, we consider the Riemann-Liouville-type general fractional derivatives of the non-singular kernel of the one-parametric Lorenzo-Hartley function. A new general fractional-order-derivative Goldstein-Kac-type telegraph equation is proposed for the first time. The analytical solution of the considered model with the graphs is obtained with the aid of the Laplace transform. The general fractional-order-derivative formula is as a new mathematical tool proposed to model the anomalous behaviors in complex and power-law phenomena.

**KEYWORDS**

PAPER SUBMITTED: 2020-03-01

PAPER REVISED: 2020-05-11

PAPER ACCEPTED: 2020-05-27

PUBLISHED ONLINE: 2020-11-27

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**Issue 6**, PAGES [3893 - 3898]

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