## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Conformable fractional derivative and its application to fractional Klein-Gordon equation

**ABSTRACT**

This paper adopts conformable fractional derivative to describe the fractional Klein-Gordon equations. The conformable fractional derivative is a new simple well-behaved definition. The fractional complex transform and variational iteration method are used to solve the fractional equation. The result shows that the proposed technology is very powerful and efficient for fractional differential equations.

**KEYWORDS**

PAPER SUBMITTED: 2018-10-11

PAPER REVISED: 2019-01-11

PAPER ACCEPTED: 2019-01-28

PUBLISHED ONLINE: 2019-06-08

- Yang, X.J. Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, (2012)
- Chen,W., Time-Space Fabric Underlying Anomalous Diffusion, Chaos Soliton and Fractals, 28(2006),pp. 923-929
- Yang, X. J., et al., A New Insight into Complexity from the Local Fractional Calculus View Point: Modelling Growths of Populations, Mathematical Methods in the Applied Sciences, 40(2017) , 17, pp.6070-6075
- Yang, X. J., et al., A New Family of the Local Fractional PDEs, Fundamenta Informaticae, 151(2017), 1-4, pp.63-75
- Khalil, R., et al., A New Definition of Fractional Derivative, Journal of Computational and Applied Mathematics, 264(2014), July, pp.65-70
- Abdeljawad, T., On Conformable Fractional Calculus, Journal of Computational and Applied Mathematics, 279(2015), May, pp.57-66
- He, J. H., A Short Remark on Fractional Variational Iteration Method, Physics Letters A, 375(2011), pp.3362-3364
- Li, Z. B., et al., Fractional Complex Transform for Fractional Differential Equations, Mathematical and Computational Applications, 15(2010), 5, pp.970-973
- Yang, X. J., et al., Non-Differentiable Exact Solutions for the Nonlinear Odes Defined on Fractal Sets, Fractals, 25(2017), 04, Artcle ID1740002
- Yang, X. J., et al., New Analytical Solutions for Klein-Gordon and Helmholtz Equations in Fractal Dimensional Space, Proceedings of the Romanian Academy Series A, 18(2017), 3, pp.231-238
- Yusufoglu, E., The Variational Iteration Method for Studying the Klein-Gordon Equation, Applied Mathematics Letter, 21(2008), 7, pp.669-674