The Experts below are selected from a list of 2058 Experts worldwide ranked by ideXlab platform
Jinrong Wang - One of the best experts on this subject based on the ideXlab platform.
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hyers ulam stability and existence of solutions for differential equations with caputo fabrizio fractional derivative
Mathematics, 2019Co-Authors: Kui Liu, Michal Fečkan, Donal Oregan, Jinrong WangAbstract:In this paper, the Hyers–Ulam stability of linear Caputo–Fabrizio fractional differential equation is established using the Laplace transform method. We also derive a generalized Hyers–Ulam stability result via the Gronwall Inequality. In addition, we establish existence and uniqueness of solutions for nonlinear Caputo–Fabrizio fractional differential equations using the generalized Banach fixed point theorem and Schaefer’s fixed point theorem. Finally, two examples are given to illustrate our main results.
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ulam hyers mittag leffler stability for ψ hilfer fractional order delay differential equations
Advances in Difference Equations, 2019Co-Authors: Kui Liu, Jinrong Wang, Donal OreganAbstract:In this paper, we present results on the existence, uniqueness, and Ulam–Hyers–Mittag-Leffler stability of solutions to a class of ψ-Hilfer fractional-order delay differential equations. We use the Picard operator method and a generalized Gronwall Inequality involved in a ψ-Riemann–Liouville fractional integral. Finally, we give two examples to illustrate our main theorems.
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Ulam–Hyers–Mittag-Leffler stability for ψ-Hilfer fractional-order delay differential equations
SpringerOpen, 2019Co-Authors: Kui Liu, Jinrong Wang, Donal O’reganAbstract:Abstract In this paper, we present results on the existence, uniqueness, and Ulam–Hyers–Mittag-Leffler stability of solutions to a class of ψ-Hilfer fractional-order delay differential equations. We use the Picard operator method and a generalized Gronwall Inequality involved in a ψ-Riemann–Liouville fractional integral. Finally, we give two examples to illustrate our main theorems
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Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative
MDPI AG, 2019Co-Authors: Kui Liu, Michal Fečkan, Donal O’regan, Jinrong WangAbstract:In this paper, the Hyers–Ulam stability of linear Caputo–Fabrizio fractional differential equation is established using the Laplace transform method. We also derive a generalized Hyers–Ulam stability result via the Gronwall Inequality. In addition, we establish existence and uniqueness of solutions for nonlinear Caputo–Fabrizio fractional differential equations using the generalized Banach fixed point theorem and Schaefer’s fixed point theorem. Finally, two examples are given to illustrate our main results
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BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS INVOLVING CAPUTO DERIVATIVE IN BANACH SPACES
Journal of Applied Mathematics and Computing, 2011Co-Authors: Jinrong Wang, Yong ZhouAbstract:In this paper, we study boundary value problems for fractional differential equations involving Caputo derivative in Banach spaces. A generalized singular type Gronwall Inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence of solutions are established by virtue of fractional calculus and fixed point method under some mild conditions. Two examples are given to illustrate the results.
Omar M. Knio - One of the best experts on this subject based on the ideXlab platform.
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Well-posedness of time-fractional, advection-diffusion-reaction equations
Fractional Calculus and Applied Analysis, 2019Co-Authors: William Mclean, Kassem Mustapha, Raed Ali, Omar M. KnioAbstract:We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our analysis relies on novel energy methods in combination with a fractional Gronwall Inequality and properties of fractional integrals.
E. Capelas Oliveira - One of the best experts on this subject based on the ideXlab platform.
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On the Stability of a Hyperbolic Fractional Partial Differential Equation
Differential Equations and Dynamical Systems, 2019Co-Authors: J. Vanterler Da C. Sousa, E. Capelas OliveiraAbstract:In this paper, the $$\psi $$ ψ -Riemann–Liouville fractional partial integral and the $$\psi $$ ψ -Hilfer fractional partial derivative are introduced and some of its particular cases are recovered. Using the Gronwall Inequality and these results, we investigate the Ulam–Hyers and Ulam–Hyers–Rassias stabilities of the solutions of a fractional partial differential equation of hyperbolic type in a Banach space $$({\mathbb {B}}, \left| \cdot \right| )$$ ( B , · ) , real or complex. Finally, we present an example in order to elucidate the results obtained.
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Mild and strong solutions for Hilfer evolution equation
arXiv: Classical Analysis and ODEs, 2019Co-Authors: J. Vanterler Da C. Sousa, Leandro S. Tavares, E. Capelas OliveiraAbstract:In this paper, we investigate the existence and uniqueness of mild and strong solutions of fractional semilinear evolution equations in the Hilfer sense, by means of Banach fixed point theorem and the Gronwall Inequality.
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Fractional order pseudoparabolic partial differential equation: Ulam-Hyers stability
arXiv: Classical Analysis and ODEs, 2018Co-Authors: J. Vanterler Da C. Sousa, E. Capelas OliveiraAbstract:Using Gronwall Inequality we will investigate the Ulam-Hyers and generalized Ulam-Hyers-Rassias stabilities for the solution of a fractional order pseudoparabolic partial differential equation.
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A Gronwall Inequality and the Cauchy-type problem by means of $\psi$-Hilfer operator
arXiv: Classical Analysis and ODEs, 2017Co-Authors: J. Vanterler Da C. Sousa, E. Capelas OliveiraAbstract:In this paper, we propose a generalized Gronwall Inequality through the fractional integral with respect to another function. The Cauchy-type problem for a nonlinear differential equation involving the $\psi$-Hilfer fractional derivative and the existence and uniqueness of solutions are discussed. Finally, through generalized Gronwall Inequality, we prove the continuous dependence of data on the Cauchy-type problem.
Jiang Wei - One of the best experts on this subject based on the ideXlab platform.
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Finite-Time Stability of Neutral Fractional Time-Delay Systems via Generalized Gronwalls Inequality
Abstract and Applied Analysis, 2014Co-Authors: Pang Denghao, Jiang WeiAbstract:This paper studies the finite-time stability of neutral fractional time-delay systems. With the generalized Gronwall Inequality, sufficient conditions of the finite-time stability are obtained for the particular class of neutral fractional time-delay systems.
Soonmo Jung - One of the best experts on this subject based on the ideXlab platform.
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on the hyers ulam stability of differential equations of second order
Abstract and Applied Analysis, 2014Co-Authors: Qusuay H Alqifiary, Soonmo JungAbstract:By using of the Gronwall Inequality, we prove the Hyers-Ulam stability of differential equations of second order with initial conditions.
