The Experts below are selected from a list of 59718 Experts worldwide ranked by ideXlab platform
A.s. Vatsala - One of the best experts on this subject based on the ideXlab platform.
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monotone Iterative Technique for finite systems of nonlinear riemann liouville fractional differential equations
Opuscula Mathematica, 2011Co-Authors: Zachary Denton, A.s. VatsalaAbstract:Comparison results of the nonlinear scalar Riemann-Liouville fractional dier- ential equation of order q, 0 < q 1, are presented without requiring Holder continuity assumption. Monotone method is developed for finite systems of fractional dierential equa- tions of order q, using coupled upper and lower solutions. Existence of minimal and maximal solutions of the nonlinear fractional dierential system is proved.
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Monotone Iterative Technique for fractional differential equations with periodic boundary conditions
Opuscula Mathematica, 2009Co-Authors: Josimar Ramirez, A.s. VatsalaAbstract:In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary conditions in the weighted norm.
Guotao Wang - One of the best experts on this subject based on the ideXlab platform.
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successive iterations and positive extremal solutions for a hadamard type fractional integro differential equations on infinite domain
Applied Mathematics and Computation, 2017Co-Authors: Ke Pei, Guotao Wang, Yanyan SunAbstract:A Hadamard type fractional integro-differential equation on infinite intervals is considered. By using monotone Iterative Technique, we not only get the existence of positive solutions, but also seek the positive minimal and maximal solutions and get two explicit monotone Iterative sequences which converge to the extremal solutions. At last, to illustrative the main result, an example is also discussed.
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monotone Iterative method for a class of nonlinear fractional differential equations on unbounded domains in banach spaces
Filomat, 2017Co-Authors: Lihong Zhang, Bashir Ahmad, Guotao WangAbstract:In this paper, we investigate the existence of minimal nonnegative solution for a class of nonlinear fractional integro-differential equations on semi-infinite intervals in Banach spaces by applying the cone theory and the monotone Iterative Technique. An example is given for the illustration of main results.
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explicit iteration to hadamard fractional integro differential equations on infinite domain
Advances in Difference Equations, 2016Co-Authors: Guotao Wang, Ke Pei, Dumitru BaleanuAbstract:This paper investigates the existence of the unique solution for a Hadamard fractional integral boundary value problem of a Hadamard fractional integro-differential equation with the monotone Iterative Technique. Two examples to illustrate our result are given.
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monotone Iterative Technique for a nonlinear fractional q difference equation of caputo type
Advances in Difference Equations, 2016Co-Authors: Guotao Wang, Lihong Zhang, Weerawat Sudsutad, Jessada TariboonAbstract:By establishing a comparison theorem and applying the monotone Iterative Technique combined with the method of lower and upper solutions, we investigate the existence of extremal solutions of the initial value problem for fractional q-difference equation involving Caputo derivative. An example is presented to illustrate the main result.
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explicit iteration and unbounded solutions for fractional integral boundary value problem on an infinite interval
Applied Mathematics Letters, 2015Co-Authors: Guotao WangAbstract:Abstract By employing the monotone Iterative Technique, we not only establish the existence of the unique solution for a fractional integral boundary value problem on semi-infinite intervals, but also develop an explicit Iterative sequence for approximating the solution and give an error estimate for the approximation, which is an important improvement of existing results.
Lihong Zhang - One of the best experts on this subject based on the ideXlab platform.
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monotone Iterative method for a class of nonlinear fractional differential equations on unbounded domains in banach spaces
Filomat, 2017Co-Authors: Lihong Zhang, Bashir Ahmad, Guotao WangAbstract:In this paper, we investigate the existence of minimal nonnegative solution for a class of nonlinear fractional integro-differential equations on semi-infinite intervals in Banach spaces by applying the cone theory and the monotone Iterative Technique. An example is given for the illustration of main results.
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monotone Iterative Technique for a nonlinear fractional q difference equation of caputo type
Advances in Difference Equations, 2016Co-Authors: Guotao Wang, Lihong Zhang, Weerawat Sudsutad, Jessada TariboonAbstract:By establishing a comparison theorem and applying the monotone Iterative Technique combined with the method of lower and upper solutions, we investigate the existence of extremal solutions of the initial value problem for fractional q-difference equation involving Caputo derivative. An example is presented to illustrate the main result.
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neutral fractional integro differential equation with nonlinear term depending on lower order derivative
Journal of Computational and Applied Mathematics, 2014Co-Authors: Guotao Wang, Sanyang Liu, Lihong ZhangAbstract:By applying an Iterative Technique, sufficient conditions are obtained for the existence of the unique solution of the nonlinear neutral fractional integro-differential equation involving two Riemann-Liouville derivatives of different fractional orders. Finally, an example is also given to illustrate the availability of our main results.
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monotone Iterative method for a class of nonlinear fractional differential equations
Fractional Calculus and Applied Analysis, 2012Co-Authors: Guotao Wang, Dumitru Baleanu, Lihong ZhangAbstract:By applying the monotone Iterative Technique and the method of lower and upper solutions, this paper investigates the existence of extremal solutions for a class of nonlinear fractional differential equations, which involve the Riemann-Liouville fractional derivative Dqx(t). A new comparison theorem is also build. At last, an example is given to illustrate our main results.
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systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions
Nonlinear Analysis-theory Methods & Applications, 2011Co-Authors: Guotao Wang, Lihong Zhang, Guangxing SongAbstract:Abstract This paper is concerned with the existence of solutions for systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions. By establishing new comparison results and applying the monotone Iterative Technique, we obtain the sufficient conditions for the existence of extremal system of solutions.
Ronald G Hadley - One of the best experts on this subject based on the ideXlab platform.
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the complex jacobi Iterative method for three dimensional wide angle beam propagation
Optics Express, 2008Co-Authors: R Godoyrubio, Peter Bienstman, Ronald G HadleyAbstract:A new complex Jacobi Iterative Technique adapted for the solution of three-dimensional (3D) wide-angle (WA) beam propagation is presented. The beam propagation equation for analysis of optical propagation in waveguide structures is based on a novel modified Pade(1,1) approximant operator, which gives evanescent waves the desired damping. The resulting approach allows more accurate approximations to the true Helmholtz equation than the standard Pade approximant operators. Furthermore, a performance comparison of the traditional direct matrix inversion and this new Iterative Technique for WA-beam propagation method is reported. It is shown that complex Jacobi iteration is faster and better-suited for large problems or structures than direct matrix inversion.
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3d wide angle beam propagation using complex jacobi iteration
Integrated Photonics Research and Applications Nanophotonics for Information Systems (2005) paper IME2, 2005Co-Authors: Ronald G HadleyAbstract:A new Iterative Technique recently developed for solution of the Helmholtz Equation is adapted for solution of 3D wide-angle beam propagation. The method is targeted towards large problems or structures with frequently-changing boundaries.
Ivan Szanto - One of the best experts on this subject based on the ideXlab platform.
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monotone Iterative Technique for riemann liouville fractional integro differential equations with advanced arguments
Results in Mathematics, 2013Co-Authors: Zhenhai Liu, Jihua Sun, Ivan SzantoAbstract:In this paper, we consider existence and uniqueness of solutions for nonlinear boundary value problems involving Riemann–Liouville fractional integro-differential equations with advanced arguments. By establishing a new comparison theorem and applying the monotone Iterative Technique, we show the existence of extremal solutions.
