Fractional Langevin equation with anti-periodic boundary conditions

Fazli, Hossein; Nieto, Juan J.

doi:10.1016/j.chaos.2018.07.009

Cited by 85 publications

(59 citation statements)

References 23 publications

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“…A particular model of the GLE is the fractional nonlinear Langevin equation (FNLE), which is another appealing subject. Many researchers studied generalized nonlinear Langevin equation with fractional derivative [11][12][13][14][15][16][17][18][19]. For instance, in [13], an application of fractional generalized nonlinear Langevin equation was studied by Eab and Lim.…”

Section: Introductionmentioning

confidence: 99%

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Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators

2020

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A new form of nonlinear Langevin equation (NLE), featuring two derivatives of non-integer orders, is studied in this research. An existence conclusion due to the nonlinear alternative of Leray-Schauder type (LSN) for the solution is offered first and, following that, the uniqueness of solution using Banach contraction principle (BCP) is demonstrated. Eventually, the derivatives of non-integer orders are elaborated in Atangana-Baleanu sense.

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Section: Introductionmentioning

confidence: 99%

“…The NLE featuring two or three derivative with non-integer orders was studied and investigated in [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators

2020

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“…Recently, several contributions mindful with the uniqueness and existence results for fractional generalized Langevin equations, have been published, see [6][7][8][9][10][11][12][13][14][15] and the references given therein.…”

Section: Introductionmentioning

confidence: 99%

Multi-Point and Anti-Periodic Conditions for Generalized Langevin Equation with Two Fractional Orders

Salem

Alghamdi

2019

Fractal Fract

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With anti-periodic and a new class of multi-point boundary conditions, we investigate, in this paper, the existence and uniqueness of solutions for the Langevin equation that has Caputo fractional derivatives of two different orders. Existence of solutions is obtained by applying Krasnoselskii–Zabreiko’s and the Leray–Schauder fixed point theorems. The Banach contraction mapping principle is used to investigate the uniqueness. Illustrative examples are provided to apply of the fundamental investigations.

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“…Lim et al [27] introduced a new form of Langevin equation containing two different fractional orders, which has made it possible to investigate fractal processes in a more flexible environment. For some recent works on fractional Langevin equation, see the papers [28][29][30][31][32][33][34][35][36] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders

2019

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In this paper we develop the existence theory for a nonlinear Langevin equation involving Caputo fractional derivatives of different orders and Riemann-Liouville fractional integral supplemented with nonlocal multi-point and multi-strip boundary conditions. We make use of the modern methods of functional analysis to obtain the existence and uniqueness results for the given problem, which are well illustrated with the aid of examples. Our results are new and correspond to some new ones for specific choices of the parameters involved in the problem. Publisher's NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Fractional Langevin equation with anti-periodic boundary conditions

Cited by 85 publications

References 23 publications

Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators

Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators

Multi-Point and Anti-Periodic Conditions for Generalized Langevin Equation with Two Fractional Orders

On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders

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