Positive solutions for integral nonlinear boundary value problem in fractional Sobolev spaces. (12th July 2021)

• Record Type: Journal Article
• Authors: Azzaoui, Bouchra; Tellab, Brahim; Zennir, Khaled
• Other Names: Gao Feng guestEditor.; Feng Wenying guestEditor.; Zhang Xinguang guestEditor.; Ge Fudong guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 3(2023)
• Page Start: 3115
• Page End: 3131
• Publication Date: 2021-07-12
• Subjects: boundary value problem -- fractional Sobolev spaces -- lower solution -- positive solutions -- upper solution; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7623
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In the present paper, we consider an important problem from the point of view of application in sciences and engineering, namely, Riemann–Liouville nonlinear fractional boundary value problem. Under new minimal conditions on the parameters 0 ≤ s, τ ≤ 1, it is shown that, based on the upper and lower solutions method using Schauder fixed point theorem, the positive solutions in a Sobolev spaces exist. Moreover, our results are illustrated by a numerical example.