Fixed Point Results and its Applications to the Systems of Non-linear Integral and Differential Equations of Arbitrary Order

Volume 9, Issue 6, pp 4949--4962 http://dx.doi.org/10.22436/jnsa.009.06.128

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Authors

Muhammad Shoaib - Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan. Muhammad Sarwar - Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan. Kamal Shah - Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan. Poom Kumam - KMUTT Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand. - KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand. - Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan.

Abstract

In this manuscript, common fixed point results for self-mappings satisfying generalized weak integral type contraction in the setting of G-metric space are established. Using the derived results, some applications to the systems of non-linear integral and fractional differential equations are also discussed.

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Keywords

• G-metric space
• integral type contraction
• alternating distance function
• integral equations
• fractional differential equations.

MSC

•  47H10
•  54H25

References

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