Now showing 1 - 10 of 11
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    Solutions to fractional functional differential equations with nonlocal conditions
    (01-01-2014) ;
    Sharma, Madhukant
    In this paper, we discuss the solutions to nonlocal initial value problems of fractional order functional differential equations in a Banach space. In particular, we prove the existence and uniqueness of mild and classical solutions assuming that -A generates a resolvent operator family and nonlinear part is a Lipschitz continuous function. We also investigate the global existence of the solution. At the end, a fractional order partial differential equation is given to illustrate the obtained abstract results. © 2014 Versita Warsaw and Springer-Verlag Wien.
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    On the stability of steady-states of a two-dimensional system of ferromagnetic nanowires
    (01-12-2017)
    Dwivedi, Sharad
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    We investigate the stability features of steady-states of a two-dimensional system of ferromagnetic nanowires.We constitute a systemwith the finite number of nanowires arranged on the (e1, e2) plane, where (e1, e2, e3) is the canonical basis of ℝ3. We consider two cases: in the first case, each nanowire is considered to be of infinite length, whereas in the second case, we deal with finite length nanowires to design the system. In both cases, we establish a sufficient condition under which these steady-states are shown to be exponentially stable.
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    Controllability of Sobolev type nonlinear nonlocal fractional functional integrodifferential equations
    (01-10-2015)
    Sharma, Madhukant
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    This paper deals with the controllability of mild solution for a class of Sobolev type nonlinear nonlocal fractional order functional integro-differential equations in a general Banach space X. We use fractional calculus, Krasnoselskii's fixed point theorem and semigroup theory for the main results and render the criteria for the complete controllability of considered problem. We also investigate the null controllability. An application is given to illustrate the abstract results.
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    Analysis of Fractional Functional Differential Equations of Neutral Type with Nonlocal Conditions
    (01-10-2017)
    Sharma, Madhukant
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    This work deals with the existence of solutions for a class of nonlinear nonlocal fractional functional differential equations of neutral type in Banach spaces. In particular, we prove the existence of solutions with the assumptions that the nonlinear parts satisfy locally Lipschitz like conditions and closed linear operator - A(t) generates analytic semigroup for each t≥ 0. We also investigate global existence of solution and study the continuous dependence of solution on initial data. We conclude the article with an application to the developed results.
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    On the Evolution of Transverse Domain Walls in Biaxial Magnetic Nanowires
    (01-01-2017)
    Dwivedi, Sharad
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    In this article, we analyze the dynamics of transverse domain walls in the framework of one-dimensional biaxial magnetic nanowires induced by the small applied magnetic fields. The evolution of magnetization in the nanowire is governed by the modified version of Landau-Lifshitz-Gilbert equation which consists of nonlinear dissipations namely dry-friction and viscous. We investigate the features of traveling wave solutions using the perturbation expansion technique. More precisely, we derive an expression for the zero order traveling wave solutions under the action of small and mild transverse magnetic fields.
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    On Dynamics of Current-Induced Static Wall Profiles in Ferromagnetic Nanowires Governed by the Rashba Field
    (01-03-2017)
    Dwivedi, Sharad
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    This article deals with the analytical study of propagation of static wall profiles in ferromagnetic nanowires under the effect of spin–orbit Rashba field. We consider the governing dynamics for the evolution of magnetization inside the ferromagnetic material as an extended version of Landau–Lifshitz–Gilbert–Slonczewski equation of micromagnetism. It comprises the nonlinear dissipation factors like dry-friction and viscous. We establish the threshold and Walker-type breakdown estimates of the external sources in the steady-regime and also illustrate the obtained results numerically.
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    Field-driven Motion of Ferrofluids in Ferromagnetic Nanowire under the Influence of Inertial Effects
    (01-01-2015)
    Dwivedi, Sharad
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    In this article, we investigate the field-driven motion of magnetic fluids (ferrofluids) in ferromagnetic nanowire under the influence of its own inertia. We establish the results in the framework of modified Landau-Lifschitz-Gilbert equation of micromagnetism which comprise the nonlinear dissipation factors like dry-friction and viscous. We delineate the motion in both the dynamical regimes namely the steady-state and the precessional. In the end, the physical significance of the obtained results is discussed with an aid of numerical analysis.
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    On Controllability of a Two-Dimensional Network of Ferromagnetic Ellipsoidal Samples
    (15-01-2019) ;
    Dwivedi, Sharad
    In this article, we address the problem of stability and controllability of two-dimensional network of ferromagnetic particles of ellipsoidal shapes. The dynamics of magnetization inside the ferromagnetic material is governed by the Landau–Lifschitz equation of micromagnetism which is non-linear and parabolic in nature. The control is the magnetic field generated by a dipole whose position and amplitude can be selected. In the absence of control, first we prove the exponential stability of the relevant configurations of the network. Then, we investigate the controllability by the means of external magnetic field induced by the magnetic dipole.
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    On the stability of static domain wall profiles in ferromagnetic thin film
    (01-01-2019)
    Dwivedi, Sharad
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    In this article, we consider a two-dimensional model of ferromagnetic material. Our prime goal is to analyze the stability of static domain wall configuration calculated by Walker. The dynamics of magnetization inside the material is governed by the Landau–Lifschitz equation which is nonlinear and parabolic in nature. We prove the stability of the static waves solutions for the Landau–Lifschitz equation with a simplified expression of the stray field which is not unique in general, because of the non-convexity constraint |u| = 1.
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    On stability of steady-statesfor a two-dimensional network model of ferromagnetic nanowires
    (01-01-2015)
    Dwivedi, Sharad
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    This article concerns with the mathematical study of stability properties of steady-states for a two-dimensional network model of ferromagnetic nanowires. We consider the finite network model of ferromagnetic nanowires of semi-infinite length. We derive a sufficient condition independent of the size of the network under which the relevant configurations (steady-states) of magnetization are shown to be asymptotically stable. To be precise, we establish the result under certain condition on the length between the two consecutive nanowires. We use perturbation technique and energy method to derive the result.