Lyapunov type inequalities for mixed nonlinear RiemannLiouville fractional differential equations with a forcing term
Ravi P. Agarwal,Abdullah zbekler +1 more
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TLDR
In this paper, some new Lyapunov and Hartman type inequalities for RiemannLiouville fractional differential equations of the form (aDx)(t)+p(t)x (t)1x(t)+q(t), where p, q, f are real-valued functions and 0<<1<<2.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2017-04-01 and is currently open access. It has received 22 citations till now.read more
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Journal ArticleDOI
A Note on Reverse Minkowski Inequality via Generalized Proportional Fractional Integral Operator with respect to Another Function
TL;DR: In this article, a generalized proportional fractional integral operator with respect to another function is introduced, which can be used for analysis of boundary value problems and eliminate linearization and unrealistic factors.
Journal ArticleDOI
Lyapunov type inequalities for the Riemann-Liouville fractional differential equations of higher order
Laihui Zhang,Zhaowen Zheng +1 more
TL;DR: In this paper, some Lyapunov type inequalities for Riemann-Liouville fractional differential equations of the form $$\bigl(D^{\alpha}_{a}x\bigr) (t)+p(t)-big| x(t)\big|^{\mu-1}x (t), p, q, f are real-valued functions.
Journal ArticleDOI
Generalized k -fractional conformable integrals and related inequalities
TL;DR: The generalized k-fractional conformable integrals (GKFIN) as discussed by the authors are the k-analogues of FIN and can be reduced to other fractional integrals under specific values of the parameters involved.
Journal ArticleDOI
Inequalities for n-class of functions using the Saigo fractional integral operator
Hasib Khan,Hasib Khan,Cemil Tunç,Dumitru Baleanu,Dumitru Baleanu,Aziz Khan,Abdulwasea Alkhazzan +6 more
TL;DR: The role of fractional integral operators can be found as one of the best ways to generalize the classical inequalities as mentioned in this paper, and the Saigo integral operator can be used to produce some inequalities for a class of n-decreasing positive functions.
Journal ArticleDOI
Lyapunov-type inequalities for a higher order fractional differential equation with fractional integral boundary conditions
TL;DR: The research of J. Nieto et al. as mentioned in this paper was partially supported by the Ministerio de Economia y Competitividad of Spain under grant MTM2013-43014-P, co-financed by the European Community fund FEDER, and XUNTA de Galicia under grant GRC2015-004.
References
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Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
Book
Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Journal ArticleDOI
Positive solutions for boundary value problem of nonlinear fractional differential equation
Zhanbing Bai,Haishen Lü +1 more
TL;DR: In this paper, the positive solution of nonlinear fractional difier- ential equation with semi-positive nonlinearity was investigated and the existence results of positive solution were obtained by using Krasnosel'skii flxed point theorem.
Book
Inequalities Involving Functions and Their Integrals and Derivatives
TL;DR: Gronwall inequalities in higher dimension as mentioned in this paper have been used to prove integral inequalities in other spaces: discrete, functional and abstract, and they have been shown to hold for functions with bounded derivatives.
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