THE ROLE OF BASE PATHS IN NIELSEN FIXED POINT THEORY

2012 ◽  
Vol 25 (2) ◽  
pp. 341-347
Author(s):  
Seoung Ho Lee
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Nielsen Fixed Point Theory

scholarly journals Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 59
Author(s):  
Ahmed Salem ◽  
Mohammad Alnegga
Keyword(s):  
Fixed Point ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of A Solution ◽  
New Class ◽  
Research Article ◽  
Analysis Technique ◽  
Modern Analysis

In this research article, we introduce a new class of hybrid Langevin equation involving two distinct fractional order derivatives in the Caputo sense and Riemann–Liouville fractional integral. Supported by three-point boundary conditions, we discuss the existence of a solution to this boundary value problem. Because of the important role of the measure of noncompactness in fixed point theory, we use the technique of measure of noncompactness as an essential tool in order to get the existence result. The modern analysis technique is used by applying a generalized version of Darbo’s fixed point theorem. A numerical example is presented to clarify our outcomes.

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