# On the Banach Space Techniques in the Existence and Uniqueness of the Fuzzy Fractional Klein-Gordon Equation's Solution

## Main Article Content

### Abstract

In this paper, we study the existence and uniqueness of the solution of all fuzzy fractional differential equations, which are equivalent to the fuzzy integral equation. We use the Banach space techniques in this study. Also we will show that the fuzzy fractional Klein-Gordon equation (FFKGE) is equivalent to a fuzzy integral equation. We use parametric form of FFKGE with respect to definition and give new homotopy analysis method to obtain the approximate solution of this equation.

## Article Details

### References

- A. A. Kilbas, H. M. Srivastava, J. J. Trujilo, Theory and applications of fractional differential equations, Elsevier, The Netherlands, 2006.
- A. Ebaid, Exact Solutions for the generalized klein-Gordon equation via atransformation and Exp-function method and comparison with Adomian's method. journal of computational an applied mathematics. 223 (2009), 278-290.
- E. Raicher, S. Eliezer, A. Zigler, A novel solution to the Klein-Gordon equation in the presence of astrong rotating electric field. Physics Letters B. 75 (2015), 76-81.
- L. A. Zadeh, K. Tanaka, M. Shimura, Fuzzy sets and their applications to congnitive and decision processes, The university of California, Berkeley, California, 1974.
- R. Goetschel, W. Voxman, Elementary calculus. Fuzzy sets And system. 18(1986), 31-43.
- SJ. Liao , Introduction to the homotopy analysis method. Boca Raton: chapman and Hall / cRc, 2003.
- JY Park , Yc Kwan , JV Jeong , Existence of solutions of fuzzy integral equations in Banach spaces. Fuzzy sets And systems. 72 (3) (1995), 373-378.
- R. Khalili , M.AL Horani , A. Yousef , M. Sababbeh , A new definition of fractional derivatives. J. Comput. AppL. math. 264 (2014), 65-70.
- T. Abdeljawad , M.AL Horani , R. Khalili , conformable fractional semiqroup operators. J. semiqroup Theory AppL. 2015 (2015), Article ID 7.
- T. Abdeljawad , on conformable fractional calculus. J. comput. AppL. Math. 279(1) (2015), 57-66.