Global attractivity of solutions for a nonlinear functional integral equation of fractional order in Banach space

2014 ◽  
Author(s):  
B. D. Karande
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fractional Order ◽  
Global Attractivity ◽  
Functional Integral ◽  
Nonlinear Functional

scholarly journals On Attractivity and Positivity of Solutions for Functional Integral Equations of Fractional Order

2013 ◽  
Vol 2013 ◽  
pp. 1-17
Author(s):  
Xianyong Huang ◽  
Junfei Cao
Keyword(s):  
Banach Space ◽  
Integral Equations ◽  
Fractional Order ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Functional Integral ◽  
Measures Of Noncompactness ◽  
Positivity Of Solutions ◽  
Unbounded Intervals ◽  
Functional Integral Equations

We investigate a class of functional integral equations of fractional order given byx(t)=q(t)+f1(t,x(α1(t)),x(α2(t)))+(f2(t,x(β1(t)),x(β2(t)))/Γ(α))×∫0t(t−s)α−1f3(t,s,x(γ1(s)),x(γ2(s)))ds: sufficient conditions for the existence, global attractivity, and ultimate positivity of solutions of the equations are derived. The main tools include the techniques of measures of noncompactness and a recent measure theoretic fixed point theorem of Dhage. Our investigations are placed in the Banach space of continuous and bounded real-valued functions defined on unbounded intervals. Moreover, two examples are given to illustrate our results.

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

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Reza Arab ◽  
Hemant Kumar Nashine ◽  
N. H. Can ◽  
Tran Thanh Binh
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Integral Equations ◽  
Fractional Order ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Arbitrary Measure ◽  
Functional Integral Equations

AbstractWe 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.

Attractivity results for a nonlinear functional integral equation

2011 ◽  
Vol 18 (1) ◽  
pp. 1-19
Author(s):  
Ravi P. Agarwal ◽  
Józef Banaś ◽  
Bapurao C. Dhage ◽  
Sidharth D. Sarkate
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Nonlinear Integral Equation ◽  
Global Attractivity ◽  
Functional Integral ◽  
Existence Results ◽  
Nonlinear Functional ◽  
Special Cases ◽  
Weaker Conditions ◽  
Unbounded Intervals

Abstract In this paper two existence results concerning the global attractivity and global asymptotic attractivity for a certain functional nonlinear integral equation are proved. Our existence results include several existence and attractivity results obtained earlier by Darwish and Hu–Yan as special cases under weaker conditions. A fixed point theorem of Dhage is used in formulating our main results and the characterizations of solutions are obtained in the space of functions defined, continuous and bounded on unbounded intervals.

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