9 research outputs found

    New Solutions for System of Fractional Integro-Differential Equations and Abel’s Integral Equations by Chebyshev Spectral Method

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    Chebyshev spectral method based on operational matrix is applied to both systems of fractional integro-differential equations and Abel’s integral equations. Some test problems, for which the exact solution is known, are considered. Numerical results with comparisons are made to confirm the reliability of the method. Chebyshev spectral method may be considered as alternative and efficient technique for finding the approximation of system of fractional integro-differential equations and Abel’s integral equations

    Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces

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    We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results

    Hilfer fractional evolution hemivariational inequalities with nonlocal initial conditions and optimal controls

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    In this paper, we mainly consider a control system governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition. We first establish sufficient conditions for the existence of mild solutions to the addressed control system via properties of generalized Clarke subdifferential and a fixed point theorem for condensing multivalued maps. Then we present the existence of optimal state-control pairs of the limited Lagrange optimal systems governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition. The optimal control results are derived without uniqueness of solutions for the control system

    A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

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    We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Applied Mathematics', ISSN: 0377-0427. Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication 20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515

    Controllability Problem of Fractional Neutral Systems: A Survey

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    The following article presents recent results of controllability problem of dynamical systems in infinite-dimensional space. Generally speaking, we describe selected controllability problems of fractional order systems, including approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in Hilbert spaces, controllability of nonlinear neutral fractional impulsive differential inclusions in Banach space, controllability for a class of fractional neutral integrodifferential equations with unbounded delay, controllability of neutral fractional functional equations with impulses and infinite delay, and controllability for a class of fractional order neutral evolution control systems
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