Continuation theorem of fractional order evolutionary integral equations

2002 ◽  
Vol 9 (2) ◽  
pp. 525-533 ◽  
Author(s):  
Ahmed M. A. El-Sayed ◽  
Mohamed A. E. Aly
Keyword(s):  
Integral Equations ◽  
Fractional Order ◽  
Continuation Theorem

Existence, uniqueness and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
JinRong Wang ◽  
Chun Zhu ◽  
Michal Fečkan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Fractional Order ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Limit Property ◽  
Type Integral

AbstractIn this paper, we apply certain measure of noncompactness and fixed point theorem of Darbo type to derive the existence and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order with three parameters. Moreover, we also present the uniqueness and another existence results of the solutions to the above equations. Finally, two examples are given to illustrate the obtained results.

scholarly journals Asymptotic behavior of fractional order Riemann-Liouville Volterra-Stieltjes integral equations

2015 ◽  
Vol 27 (3) ◽  
pp. 311-323
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Boualem A. Slimani ◽  
Juan J. Trujillo
Keyword(s):  
Asymptotic Behavior ◽  
Integral Equations ◽  
Fractional Order ◽  
Stieltjes Integral

scholarly journals From fractional order equations to integer order equations

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Daniel Cao Labora ◽  
Rosana Rodríguez-López
Keyword(s):  
Integral Equation ◽  
Integral Operator ◽  
Vector Space ◽  
Integral Equations ◽  
Fractional Order ◽  
Fractional Integral ◽  
State Of The Art ◽  
Constant Coefficients ◽  
Fractional Order Integral ◽  
Ordinary Integral

AbstractThe main goal of this article is to show a new method to solve some Fractional Order Integral Equations (FOIE), more precisely the ones which are linear, have constant coefficients and all the integration orders involved are rational. The method essentially turns a FOIE into an Ordinary Integral Equation (OIE) by applying a suitable fractional integral operator.After discussing the state of the art, we present the idea of our construction in a particular case (Abel integral equation). After that, we propose our method in a general case, showing that it does work when dealing with a family of “additive” operators over a vector space. Later, we show that our construction is always possible when dealing with any FOIE under the above-mentioned hypotheses. Furthermore, it is shown that our construction is “optimal” in the sense that the OIE that we obtain has the least possible order.

Fractional-order evolutionary integral equations

1999 ◽  
Vol 98 (2-3) ◽  
pp. 139-146 ◽  
Author(s):  
Ahmed M.A. El-Sayed
Keyword(s):  
Integral Equations ◽  
Fractional Order

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.

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