Symmetric Solutions of Nonlinear Fractional Integral Equations via a New Fixed Point Theorem under FG-Contractive Condition

Abstract

We set up the existence of a symmetric outcome of a system of simultaneous nonlinear fractional integral equations, that arises in motion of water wave on smooth surface, with the help of a common fixed point theorem satisfying a generalized FG-contractive condition. To accomplish this, we introduce first the concept of generalized FG-contractive condition for two pairs of self-mappings in a complete metric space and then we establish requisites for common fixed point results for weakly compatible mappings followed by a suitable example.

Keywords:

• Common fixed point
• fractional calculus
• fractional differential equation
• fractional differential operator
• weakly compatible mappings

MATHEMATICS SUBJECT CLASSIFICATION (2010):

• 47H10
• 54H25
• 26A33

Acknowledgments

The authors would like to express their thanks to the reviewers for their important and useful comments to improve the paper. Special thanks to Professor Dr. Zuhair Nashed for his kind suggestions. The first author is thankful to the United State-India Education Foundation, New Delhi, India and IIE/CIES, Washington, DC, USA for Fulbright-Nehru PDF Award (No. 2052/FNPDR/2015).