The Experts below are selected from a list of 161727 Experts worldwide ranked by ideXlab platform
Maojun Bin - One of the best experts on this subject based on the ideXlab platform.
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Approximate controllability of impulsive Riemann- Liouville fractional equations in Banach spaces
Journal of Integral Equations and Applications, 2014Co-Authors: Zhenhai Liu, Maojun BinAbstract:In this paper, we study control systems governed by impulsive Riemann-Liouville fractional differential equations in Banach spaces. Firstly, we introduce $PC_{1-\alpha}$-mild solutions for impulsive Riemann-Liouville fractional differential equations. Then, we make a set of assumptions to guarantee the existence and uniqueness of mild solutions. Finally, approximate controllability of the associated impulsive Riemann-Liouville fractional evolution control systems is also formulated and proved.
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Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions
Abstract and Applied Analysis, 2013Co-Authors: Zhenhai Liu, Maojun BinAbstract:We study the control systems governed by impulsive Riemann-Liouville fractional differential inclusions and their approximate controllability in Banach space. Firstly, we introduce the -mild solutions for the impulsive Riemann-Liouville fractional differential inclusions in Banach spaces. Secondly, by using the fractional power of operators and a fixed point theorem for multivalued maps, we establish sufficient conditions for the approximate controllability for a class of Riemann-Liouville fractional impulsive differential inclusions, which is a generalization and continuation of the recent results on this issue. At the end, we give an example to illustrate the application of the abstract results.
Ravi P. Agarwal - One of the best experts on this subject based on the ideXlab platform.
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a study of riemann liouville fractional nonlocal integral boundary value problems
Boundary Value Problems, 2013Co-Authors: Bashir Ahmad, Afrah Assolami, Ravi P. Agarwal, Ahmed AlsaediAbstract:In this paper, we discuss the existence and uniqueness of solutions for a Riemann-Liouville type fractional differential equation with nonlocal four-point Riemann-Liouville fractional-integral boundary conditions by means of classical fixed point theorems. An illustration of main results is also presented with the aid of some examples. MSC:34A08, 34B10, 34B15.
Qi-man Shao - One of the best experts on this subject based on the ideXlab platform.
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LARGE DEVIATIONS FOR LOCAL TIMES AND INTERSECTION LOCAL TIMES OF FRACTIONAL BROWNIAN MOTIONS AND RIEMANN―LIOUVILLE PROCESSES
The Annals of Probability, 2011Co-Authors: Xia Chen, Jan Rosiński, Qi-man ShaoAbstract:In this paper, we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann― Liouville processes. We also show that a fractional Brownian motion and the related Riemann―Liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times. As a consequence of our large deviation estimates, we derive laws of iterated logarithm for the corresponding local times. The key points of our methods: (1) logarithmic superadditivity of a normalized sequence of moments of exponentially randomized local time of a fractional Brownian motion; (2) logarithmic subadditivity of a normalized sequence of moments of exponentially randomized intersection local time of Riemann―Liouville processes; (3) comparison of local and intersection local times based on embedding of a part of a fractional Brownian motion into the reproducing kernel Hilbert space of the Riemann―Liouville process.
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Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes
arXiv: Probability, 2009Co-Authors: Xia Chen, Jan Rosiński, Qi-man ShaoAbstract:In this paper we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes. We also show that a fractional Brownian motion and the related Riemann-Liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times. As a consequence of our large deviation estimates, we derive laws of iterated logarithm for the corresponding local times. The key points of our methods: (1) logarithmic superadditivity of a normalized sequence of moments of exponentially randomized local time of a fractional Brownian motion; (2) logarithmic subadditivity of a normalized sequence of moments of exponentially randomized intersection local time of Riemann-Liouville processes; (3) comparison of local and intersection local times based on embedding of a part of a fractional Brownian motion into the reproducing kernel Hilbert space of the Riemann-Liouville process.
Zhenhai Liu - One of the best experts on this subject based on the ideXlab platform.
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Approximate Controllability of Fractional Evolution Systems with Riemann--Liouville Fractional Derivatives
SIAM Journal on Control and Optimization, 2015Co-Authors: Zhenhai LiuAbstract:In this paper, we deal with the control systems governed by fractional evolution differential equations involving Riemann--Liouville fractional derivatives in Banach spaces. Our main purpose in this article is to establish suitable assumptions to guarantee the existence and uniqueness results of mild solutions. Under these conditions, the approximate controllability of the associated fractional evolution systems involving Riemann--Liouville fractional derivatives is formulated and proved.
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Approximate controllability of impulsive Riemann- Liouville fractional equations in Banach spaces
Journal of Integral Equations and Applications, 2014Co-Authors: Zhenhai Liu, Maojun BinAbstract:In this paper, we study control systems governed by impulsive Riemann-Liouville fractional differential equations in Banach spaces. Firstly, we introduce $PC_{1-\alpha}$-mild solutions for impulsive Riemann-Liouville fractional differential equations. Then, we make a set of assumptions to guarantee the existence and uniqueness of mild solutions. Finally, approximate controllability of the associated impulsive Riemann-Liouville fractional evolution control systems is also formulated and proved.
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Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions
Abstract and Applied Analysis, 2013Co-Authors: Zhenhai Liu, Maojun BinAbstract:We study the control systems governed by impulsive Riemann-Liouville fractional differential inclusions and their approximate controllability in Banach space. Firstly, we introduce the -mild solutions for the impulsive Riemann-Liouville fractional differential inclusions in Banach spaces. Secondly, by using the fractional power of operators and a fixed point theorem for multivalued maps, we establish sufficient conditions for the approximate controllability for a class of Riemann-Liouville fractional impulsive differential inclusions, which is a generalization and continuation of the recent results on this issue. At the end, we give an example to illustrate the application of the abstract results.
Juan J. Nieto - One of the best experts on this subject based on the ideXlab platform.
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Global attractivity for some classes of Riemann--Liouville fractional differential systems
Journal of Integral Equations and Applications, 2019Co-Authors: H. T. Tuan, Juan J. Nieto, Adam Czornik, Michal NiezabitowskiAbstract:We present results for existence of global solutions and attractivity for multidimensional fractional differential equations involving Riemann-Liouville derivative. First, by using a Bielecki type norm and the Banach-fixed point theorem, we prove a Picard-Lindelof-type theorem on the existence and uniqueness of solutions. Then, applying the properties of Mittag-Leffler functions, we describe the attractivity of solutions to some classes of Riemann-Liouville linear fractional differential systems.
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Global attractivity for some classes of Riemann--Liouville fractional differential systems
arXiv: Classical Analysis and ODEs, 2017Co-Authors: H. T. Tuan, Juan J. Nieto, Adam Czornik, Michal NiezabitowskiAbstract:In this paper, we present some results for existence of global solutions and attractivity for mulidimensional fractional differential equations involving Riemann-Liouville derivative. First, by using a Bielecki type norm and Banach fixed point theorem, we prove a Picard-Lindelof type theorem on the existence and uniqueness of solutions. Then, applying the properties of Mittag-Leffler functions, we describe the attractivity of solutions to some classes of Riemann--Liouville linear fractional differential systems.
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The Applications of Critical-Point Theory to Discontinuous Fractional-Order Differential Equations
Proceedings of the Edinburgh Mathematical Society, 2017Co-Authors: Yu Tian, Juan J. NietoAbstract:AbstractWe consider a fractional equation involving the left and right Riemann–Liouville fractional integrals and with Sturm–Liouville boundary-value conditions. We establish the variational structure of the problem and, by using critical-point theory, the existence of an unbounded sequence of solutions is obtained.
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Projectile motion via Riemann-Liouville calculus
Advances in Difference Equations, 2015Co-Authors: Bashir Ahmad, Juan J. Nieto, Hanan Batarfi, Óscar Otero-zarraquiños, Wafa ShammakhAbstract:We present an analysis of projectile motion in view of fractional calculus. We obtain the solution for the problem using the Riemann-Liouville derivative, and then we compute some features of projectile motion in the framework of Riemann-Liouville fractional calculus. We compare the solutions using Caputo derivatives and Riemann-Liouville derivatives.
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schauder fixed point theorem in semilinear spaces and its application to fractional differential equations with uncertainty
Fixed Point Theory and Applications, 2014Co-Authors: Alireza Khastan, Juan J. Nieto, Rosana RodriguezlopezAbstract:We study the existence of solution for nonlinear fuzzy differential equations of fractional order involving the Riemann-Liouville derivative.
