On strong solutions of fractional nonlinear viscoelastic model of Voigt type
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DOI: 10.1002/mma.6359
Abstract: This paper concerns the existence and uniqueness of the strong solutions to the initial‐boundary value problems of fractional analog of Voigt model in the planar case. read more here.
Keywords: voigt; solutions fractional; strong solutions; model ... See more keywords
Numerical simulation for time‐fractional nonlinear reaction–diffusion system on a uniform and nonuniform time stepping
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DOI: 10.1002/mma.7114
Abstract: In this article, two nonstandard high‐order schemes on a uniform and nonuniform time stepping combined with the multi‐parameter exponential fitting technique (MPEF) have been developed to solve the time‐fractional nonlinear reaction–diffusion system. The first method… read more here.
Keywords: time; time stepping; nonuniform time; uniform nonuniform ... See more keywords
Design of delayed fractional state variable filter for parameter estimation of fractional nonlinear models
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DOI: 10.1007/s11071-018-4519-0
Abstract: This paper presents a novel direct parameter estimation method for continuous-time fractional nonlinear models. This is achieved by adapting a filter-based approach that uses the delayed fractional state variable filter for estimating the nonlinear model… read more here.
Keywords: state variable; parameter estimation; fractional state; fractional nonlinear ... See more keywords
A conservative numerical method for the fractional nonlinear Schröinger equation in two dimensions
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DOI: 10.1007/s11425-018-9388-9
Abstract: This paper proposes and analyzes an efficient finite difference scheme for the two-dimensional nonlinear Schrödinger (NLS) equation involving fractional Laplacian. The scheme is based on a weighted and shifted Grünwald-Letnikov difference (WSGD) operator for the… read more here.
Keywords: nonlinear schr; scheme; method; equation ... See more keywords
Approximate controllability of fractional nonlinear neutral stochastic differential inclusion with nonlocal conditions and infinite delay
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DOI: 10.1007/s40065-017-0163-7
Abstract: In this paper we consider a class of fractional nonlinear neutral stochastic evolution inclusions with nonlocal initial conditions in Hilbert space. Using fractional calculus, stochastic analysis theory, operator semigroups and Bohnenblust–Karlin’s fixed point theorem, a… read more here.
Keywords: controllability fractional; nonlinear neutral; stochastic differential; fractional nonlinear ... See more keywords
Comments on “The stability and control of fractional nonlinear system with distributed time delay” [Appl. Math. Model. 40 (2016) 3257–3263]
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DOI: 10.1016/j.apm.2017.06.036
Abstract: Abstract In this comment, we give four counterexamples to show that Conclusion 1, Conclusion 2, Theorem 1 and Theorem 2 of a recent paper [1] are incorrect. read more here.
Keywords: system distributed; comments stability; fractional nonlinear; control fractional ... See more keywords
Optical soliton solutions of perturbing time-fractional nonlinear Schrödinger equations
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DOI: 10.1016/j.ijleo.2020.164589
Abstract: Abstract This article presents a technique for finding solitary wave solutions of higher-order nonlinear differential equations. Time fractional nonlinear differential equations that have hierarchy contain higher orders are presented for the description of highly dispersive… read more here.
Keywords: solutions perturbing; time fractional; fractional nonlinear; soliton solutions ... See more keywords
Dynamical behavior and exact solutions for time-fractional nonlinear Schrödinger equation with parabolic law nonlinearity
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DOI: 10.1016/j.ijleo.2020.165331
Abstract: Abstract The time-fractional nonlinear Schrodinger equation with parabolic law nonlinearity is studied. Under the travelling wave transformations, Schrodinger equation is reduced to plane system, which is analyzed by theory of planar dynamical systems. The periodic-wave… read more here.
Keywords: time fractional; equation parabolic; fractional nonlinear; parabolic law ... See more keywords
Various optical soliton for a weak fractional nonlinear Schrödinger equation with parabolic law
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DOI: 10.1016/j.rinp.2021.103998
Abstract: Abstract In this manuscript, we study various forms of optical dromions (solitons) for a weak time fractional nonlinear Schrodinger equation (WTFNLSE) with parabolic law. We obtain various forms of solitons like as bright dromions, dromions… read more here.
Keywords: parabolic law; optical soliton; various optical; equation ... See more keywords
Stability of standing wave for the fractional nonlinear Schrödinger equation
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DOI: 10.1063/1.5021689
Abstract: In this paper, we study the stability and instability of standing waves for the fractional nonlinear Schrodinger equation i∂tu = (−Δ)su − |u|2σu, where (t,x)∈R × RN, 12 read more here.
Keywords: standing wave; wave fractional; fractional nonlinear; equation ... See more keywords
Accurate sets of solitary solutions for the quadratic–cubic fractional nonlinear Schrödinger equation
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DOI: 10.1063/5.0050624
Abstract: The analytical and semi-analytical solutions to the quadratic–cubic fractional nonlinear Schrodinger equation are discussed in this research article. The model’s fractional formula is transformed into an integer-order model by using a new fractional operator. The… read more here.
Keywords: solutions quadratic; quadratic cubic; accurate sets; fractional nonlinear ... See more keywords