Displaying similar documents to “Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation”

Existence and stability of solutions for a system of quadratic integral equations in Banach algebras

Said Baghdad (2020)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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The aim of this paper is to prove the existence and stability of solutions of a system of quadratic integral equations in the Banach algebra of continuous and bounded functions on unbounded rectangle. The main tool used in our considerations is the multiple fixed point theorem which is a consequence of Darbo's fixed point theorem and the technique associated with measures of noncompactness. We also present an illustrative example.

Quadratic integral equations in reflexive Banach space

Hussein A.H. Salem (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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This paper is devoted to proving the existence of weak solutions to some quadratic integral equations of fractional type in a reflexive Banach space relative to the weak topology. A special case will be considered.

Nonlinear Implicit Hadamard’s Fractional Differential Equationswith Delay in Banach Space

Mouffak Benchohra, Soufyane Bouriah, Jamal E. Lazreg, Juan J. Nieto (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper, we establish sufficient conditions for the existence of solutions for nonlinear Hadamard-type implicit fractional differential equations with finite delay. The proof of the main results is based on the measure of noncompactness and the Darbo’s and Mönch’s fixed point theorems. An example is included to show the applicability of our results.

Stability of Caputo fractional differential equations by Lyapunov functions

Ravi P. Agarwal, Donal O'Regan, Snezhana Hristova (2015)

Applications of Mathematics

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The stability of the zero solution of a nonlinear nonautonomous Caputo fractional differential equation is studied using Lyapunov-like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov-like function along the given fractional equation. Comparison results using this definition for scalar fractional differential equations are presented. Several sufficient conditions for stability, uniform stability and asymptotic uniform stability, based...

Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line

Amina Boucenna, Toufik Moussaoui (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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The aim of this paper is to study the existence of solutions to a boundary value problem associated to a nonlinear fractional differential equation where the nonlinear term depends on a fractional derivative of lower order posed on the half-line. An appropriate compactness criterion and suitable Banach spaces are used and so a fixed point theorem is applied to obtain fixed points which are solutions of our problem.

IVPs for singular multi-term fractional differential equations with multiple base points and applications

Yuji Liu, Pinghua Yang (2014)

Applicationes Mathematicae

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The purpose of this paper is to study global existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. By constructing a special Banach space and employing fixed-point theorems, some sufficient conditions are obtained for the global existence and uniqueness of solutions of this kind of equations involving Caputo fractional derivatives and multiple base points. We apply the results to solve the forced logistic model with multi-term...

Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems

Tadeusz Kaczorek (2016)

International Journal of Applied Mathematics and Computer Science

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Fractional descriptor reduced-order nonlinear observers for a class of fractional descriptor continuous-time nonlinear systems are proposed. Sufficient conditions for the existence of the observers are established. The design procedure for the observers is given and demonstrated on a numerical example.

On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)

Małgorzata Klimek (2011)

Banach Center Publications

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One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.