Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order

Section: Introductionmentioning

confidence: 99%

Extension of the fractional derivative operator of the Riemann-Liouville

Băleanu¹,

Agarwal²,

Parmar³

et al. 2017

“…The recent development covers the theoretical as well as potential applications of the subject in physical and technical science. Recently, Atangana and Baleanu proposed a derivative with fractional order based upon the Mittag-Leffler function which has a non-singular and nonlocal kernel, see [2,3] and the references therein. Fractional differential equations have been of great interest recently, see [6,10,11].…”

Section: Introductionmentioning

confidence: 99%

Uniqueness results for nonlinear fractional differential equations with infinite-point integral boundary conditions

Liu¹,

Liu²,

Dai³

et al. 2017

In this paper, we consider a class of nonlinear fractional differential equations involving the Riemann-Liouville fractional derivative with infinite-point integral boundary conditions. Our analysis relies on the fixed point index theory and u 0 -positive operator. An example is given for the illustration of the main work. c 2017 All rights reserved.Keywords: Fractional differential equations, infinite-point integral boundary condition, u 0 -positive operator, fixed point index theory. 2010 MSC: 26A33, 34A34.

“…Thus there are many researchers in the literature who studied and have dealt this type of problems, for example, see ( [2,5,7,8,11,12,15,16,21,22]). …”

Section: Introductionmentioning

confidence: 99%

Sufficient conditions on existence of solution for nonlinear fractional iterative integral equation

Damag¹,

Kılıçman²

2017

In this article, we study nonlinear quadratic iterative integral equations and establish sufficient conditions for the existence of Volterra solutions for fractional iterative integral equations and solvency in Banach space and C ,β . In the present work we use the principle of contraction, Schaefer's fixed point theorem and the non-expansive operator method as essential tools. In this study we consider Riemann-Liouville differential operator and prove some related theorems, further provide an example as an application. c 2017 all rights reserved.Keywords: Fractional integral equation, existence of solution, Schaefer's fixed point theorem, non-expansive operator.