Solvability of functional-integral equations (fractional order) using measure of noncompactness

Advances in Difference Equations

article

Arab, Reza¹  Nashine, Hemant Kumar²  Can, N. H.⁴  Binh, Tran Thanh⁵ 

[1] Department of Mathematics, Sari Branch, Islamic Azad University;Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology;Department of Pure and Applied Mathematics, Faculty of Science, University of Johannesburg;Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University;Institute of Research and Development, Duy Tan University

关键词: Fixed point;    Measure of noncompactness;    Functional-integral equation;   

DOI  :  10.1186/s13662-019-2487-4

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contraction operator and derive generalized Darbo fixed point results using an arbitrary measure of noncompactness in Banach spaces. An illustration is given in support of the solution of a functional-integral equation of fractional order.

【 授权许可】

CC BY