Stable monotone iterative solutions to a class of boundary value problems of nonlinear fractional order differential equations

Volume 12, Issue 6, pp 376--386 http://dx.doi.org/10.22436/jnsa.012.06.04

Publication Date: January 30, 2019 Submission Date: September 16, 2018 Revision Date: November 16, 2018 Accteptance Date: December 14, 2018

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Authors

Sajjad Ali - Department of Mathematics, Abdul Wali Khan University of Mardan, Khyber Pakhtunkhwa, Pakistan. Muhammad Arif - Department of Mathematics, Abdul Wali Khan University of Mardan, Khyber Pakhtunkhwa, Pakistan. Durdana Lateef - Department of Mathematics, College of Science, Taibah University, Madinah, KSA. Mohammad Akram - Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, KSA.

Abstract

We construct sufficient conditions for existence of extremal solutions to boundary value problem (BVP) of nonlinear fractional order differential equations (NFDEs). By combing the method of lower and upper solution with the monotone iterative technique, we construct sufficient conditions for the iterative solutions to the problem under consideration. Some proper results related to Hyers-Ulam type stability are investigated. Base on the proposed method, we construct minimal and maximal solutions for the proposed problem. We also construct and provide maximum error estimates and test the obtain results by two examples.

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Keywords

• Nonlinear fractional differential equations
• iterative technique
• upper and lower solutions
• uniqueness and existence

MSC

•  34A08
•  34A45

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