A nonlocal three-point inclusion problem of Langevin equation with two different fractional orders

Advances in Difference Equations

Ahmed Alsaedi¹  Juan J Nieto²  Bashir Ahmad² 

[1] Departamento de AnáDepartment of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;lisis Matemisáticas, Universidad de Santiago de Compostela, Santiago de Compostela, Spain;tico, Facultad de Matemá

关键词: Langevin equation;    fractional order;    inclusions;    nonlocal boundary conditions;    fixed point theorems;   

DOI  :  10.1186/1687-1847-2012-54

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This article studies the existence of solutions for a three-point inclusion problem of Langevin equation with two fractional orders. Our main tools of study include a nonlinear alternative of Leray-Schauder type, selection theorem due to Bressan and Colombo for lower semicontinuous multivalued maps, and a fixed point theorem for multivalued map due to Covitz and Nadler. An illustrative example is also presented. Mathematical Subject Classification 2000: 26A33; 34A12; 34A40.

【 授权许可】

CC BY