Existence of solution and Hyers-Ulam stability for a coupled system of fractional differential equations with \(p\)-Laplacian operator

Volume 10, Issue 10, pp 5219--5229 http://dx.doi.org/10.22436/jnsa.010.10.08

Publication Date: October 14, 2017 Submission Date: July 15, 2017

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Authors

Hasib Khan - State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, 210098, Nanjing, P. R. China. - Shaheed Benazir Bhutto University Sheringal, Dir Upper, 18000, Khyber Pakhtunkhwa, Pakistan. Yongjin Li - Department of Mathematics, Sun Yat-sen University, 510275, Guangzhou, P. R. China. Hongguang Sun - State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, 210098, Nanjing, P. R. China. Aziz Khan - Department of Mathematics, University of Peshawar, 25000, Khyber Pakhtunkhwa, Pakistan.

Abstract

Models with \(p\)-Laplacian operator are common in different scientific fields including; plasma physics, chemical reactions design, physics, biophysics, and many others. In this paper, we investigate existence and uniqueness of solution and Hyers-Ulam stability for a coupled system of fractional differential equations with \(p\)-Laplacian operator. The Hyers-Ulam stability means that a differential equation has a close exact solution which is generated by the approximate solution of the differential equation and the error in the approximation can be estimated. We use topological degree method and provide an expressive example as an application of the work.

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Keywords

• Existence and uniqueness of solution
• Hyers-Ulam stability
• topological degree method
• \(p\)-Laplacian operator

MSC

•  47H10
•  54H25

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