Abstract
This paper is concerned with the existence and uniqueness of positive solutions for a Volterra nonlinear fractional system of integral equations. Our analysis relies on a fixed point theorem of a sum operator. The conditions for the existence and uniqueness of a positive solution to the system are established. Moreover, an iterative scheme is constructed for approximating the solution. The case of quadratic system of fractional integral equations is also considered.
Highlights
Fractional calculus has been used for the study of problems in various fields of sciences, such as Abel integral equation and viscoelasticity, analysis of feedback amplifiers, capacitor theory, fractances, generalized voltage dividers, and engineering and biological sciences
The aim of this paper is to study the existence and uniqueness of positive solutions for the following Volterra nonlinear fractional system of integral equations: xi (t) =
By using a fixed point theorem of a sum operator, we obtain the existence and uniqueness of positive solutions for the system (4), and construct some sequences for approximating the unique solution
Summary
Fractional calculus has been used for the study of problems in various fields of sciences, such as Abel integral equation and viscoelasticity, analysis of feedback amplifiers, capacitor theory, fractances, generalized voltage dividers, and engineering and biological sciences. Salem [17] applied Krasnoselskii’s fixed point theorem to obtain the existence of solutions for the system: xi (t) = φi (t) + λiIαi [fi (x (t)) + gi (x (t))] , (2) The aim of this paper is to study the existence and uniqueness of positive solutions for the following Volterra nonlinear fractional system of integral equations: xi (t) =
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