Shruti Dubey

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In this article, we investigate the static properties of the transverse domain wall in ferromagnetic nanostrip under the influence of a uniform transverse magnetic field. We perform the analysis under the framework of the Landau–Lifshitz–Gilbert equation, which describes the evolution of magnetization inside the ferromagnetic medium. More precisely, first, we establish the magnetization profile in the two faraway domains and then examine the static magnetization profile in the sole presence of the applied transverse magnetic field, both analytically and numerically. The obtained analytical results are in qualitatively good agreement with recent numerical simulations and experimental observations.

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.

A higher-order finite difference method is developed to solve the variable coefficients convection–diffusion singularly perturbed problems (SPPs) involving fractional-order time derivative with the order α∈(0,1). The solution to this problem class possesses a typical weak singularity at the initial time t=0 and an exponential boundary layer at the right lateral surface as the perturbation parameter ɛ→0. Alikhanov's L2−1σ approximation is applied in the temporal direction on a suitable graded mesh, and the spatial variable is discretized on a piecewise uniform Shishkin mesh using a combination of midpoint upwind and central finite difference operators. Stability estimates and the convergence analysis of the fully discrete scheme are provided. It is shown that the fully discrete scheme is uniformly convergent with a rate of O(M−p+N−2(logN)2), where p=min{2,rα}, r is the graded mesh parameter and M,N are the number of mesh points in the time and space direction, respectively. Two numerical examples are taken in counter to confirm the sharpness of the theoretical estimates.

In this paper, we first characterize the behaviour of fractional resolvent families on the real interpolation spaces (X,D(A))θ,p,θ∈(0,1),p∈[1,∞]. Second, we establish strict Hölder regularity in space and time to an abstract degenerate fractional order differential equations. We also provide an application to illustrate our results.

In this paper, the invariant subspace method (ISM) is developed to obtain the exact solution of linear and nonlinear time and space fractional mixed partial differential equations involving modified conformable fractional derivative (MCFD). Moreover, the method is successfully extended to the coupled system of modified conformable fractional differential equations. Variety of time-space fractional mixed PDEs are considered and solved to illustrate the established result of ISM. Finally, a comparison between exact solution of fractional PDE in the sense of MCFD and Caputo fractional derivative (Ca-FD) is presented through some examples of time–space fractional mixed partial differential equations.

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.

In this paper, an efficient orthogonal neural network (ONN) approach is introduced to solve the higher-order neutral delay differential equations (NDDEs) with variable coefficients and multiple delays. The method is implemented by replacing the hidden layer of the feed-forward neural network with the orthogonal polynomial-based functional expansion block, and the corresponding weights of the network are obtained using an extreme learning machine(ELM) approach. Starting with simple delay differential equations (DDEs), an interest has been shown in solving NDDEs and system of NDDEs. Interest is given to consistency and convergence analysis, and it is seen that the method can produce a uniform closed-form solution with an error of order 2 -n, where n is the number of neurons. The developed neural network method is validated over various types of example problems(DDEs, NDDEs, and system of NDDEs) with four different types of special orthogonal polynomials.

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.

This work reveals an analytical investigation of the curved domain wall motion in ferromagnetic nanostructures in the framework of the extended Landau-Lifshitz-Gilbert equation. To be precise, the study delineates the description of curved domain wall motion in the steady-state dynamic regime for metallic and semiconductor ferromagnets. The study is done under the simultaneous action of the Rashba field and nonlinear dissipative effects described via the viscous-dry friction mechanism. By means of reductive perturbation technique and realistic assumption on the considered parameters, we establish an analytical expression of the steady domain wall velocity that depends on mean curvature of domain wall surfaces, nonlinear dissipation coefficients, Rashba parameter, external magnetic field, and spin-polarized electric current. In particular, it is observed that the domain wall velocity, mobility, threshold, and Walker breakdown can be manipulated by the combined mechanism of the Rashba field and nonlinear dissipation coefficients. Finally, the obtained analytical results are illustrated numerically for the curved domain walls through constant-curvature surfaces under-considered scenarios. The results presented herein are in qualitatively good agreement with the recent observations.