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

Khan, Hasib ¹ ; Li, Yongjin ² ; Sun, Hongguang ³ ; Khan, Aziz ⁴

¹ 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
² Department of Mathematics, Sun Yat-sen University, 510275, Guangzhou, P. R. China
³ State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, 210098, Nanjing, P. R. China
⁴ Department of Mathematics, University of Peshawar, 25000, Khyber Pakhtunkhwa, Pakistan

Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 10, p. 5219-5229.

Résumé

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.

Détail

DOI : 10.22436/jnsa.010.10.08

Classification : 47H10, 54H25
Keywords: Existence and uniqueness of solution, Hyers-Ulam stability, topological degree method, \(p\)-Laplacian operator

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