Analysis of positive solution and Hyers-Ulam stability for a class of singular fractional differential equations withp-Laplacian in Banach space

2018 ◽  
Vol 41 (9) ◽  
pp. 3430-3440 ◽  
Author(s):  
Hasib Khan ◽  
Wen Chen ◽  
Hongguang Sun
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Positive Solution ◽  
Fractional Differential Equations ◽  
Ulam Stability ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential

scholarly journals On Generalized Hyers-Ulam Stability of Admissible Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Banach Spaces ◽  
Unit Disk ◽  
Fractional Differential Equations ◽  
Complex Banach Space ◽  
Ulam Stability ◽  
Fractional Operators ◽  
Fractional Differential ◽  
Admissible Functions

We consider the Hyers-Ulam stability for the following fractional differential equations in sense of Srivastava-Owa fractional operators (derivative and integral) defined in the unit disk:Dzβf(z)=G(f(z),Dzαf(z),zf'(z);z),0<α<1<β≤2, in a complex Banach space. Furthermore, a generalization of the admissible functions in complex Banach spaces is imposed, and applications are illustrated.

GENERALIZED ULAM–HYERS STABILITY FOR FRACTIONAL DIFFERENTIAL EQUATIONS

2012 ◽  
Vol 23 (05) ◽  
pp. 1250056 ◽  
Author(s):  
RABHA W. IBRAHIM
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Complex Banach Space ◽  
Ulam Stability ◽  
Fractional Differential

In the present paper, we consider the generalized Hyers–Ulam stability for fractional differential equations of the form: [Formula: see text] in a complex Banach space. Furthermore, applications are illustrated.

scholarly journals Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach Space

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Bo Liu ◽  
Yansheng Liu
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Sufficient Condition ◽  
Point Boundary ◽  
Approximate Problem ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential

This paper investigates the existence of positive solutions to a two-point boundary value problem (BVP) for singular fractional differential equations in Banach space and presents a number of new results. First, by constructing a novel cone and using the fixed point index theory, a sufficient condition is established for the existence of at least two positive solutions to the approximate problem of the considered singular BVP. Second, using Ascoli-Arzela theorem, a sufficient condition is obtained for the existence of at least two positive solutions to the considered singular BVP from the convergent subsequence of the approximate problem. Finally, an illustrative example is given to support the obtained new results.

Sign in / Sign up

Export Citation Format

Share Document