Fractional dynamics of an erbium-doped fiber laser model

Gómez-Aguilar, J. F.; Saad, Khaled M.; Băleanu, Dumitru

doi:10.1007/s11082-019-2033-3

Cited by 12 publications

(3 citation statements)

References 23 publications

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“…Also, optical solutions can be constructed to explain many phenomena in optics or other areas. [1][2][3][4][5][6][7][8] The analysis of traveling wave solutions of nonlinear evolution equations is developing expeditiously because optical modeling of many physical systems leads to nonlinear evolution flows. They are experienced in a diversity of optics and modeled applications such as fluid dynamics, optical fibers, plasma physics, chemical physics, oceans engineering, biomathematics, and many other mathematical fields.…”

Section: Introductionmentioning

confidence: 99%

“…The optical solutions of nonlinear Schrödinger equations are significant in the optical phase, propagation of optical pulses in optical fibers, optical communication areas, electromagnetism, ultrashort optical solitons propagation in the nonlinear phase, plasma, and fluid flow. Also, optical solutions can be constructed to explain many phenomena in optics or other areas 1–8 …”

Section: Introductionmentioning

confidence: 99%

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New approach for propagated light with optical solitons by optical fiber in pseudohyperbolic space ℍ02

Körpınar

Băleanu

et al. 2021

Math Methods in App Sciences

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In this paper, a new evolution of polarized light ray by optical fiber in the pseudohyperbolic space H 2 0 is examined. Firstly, the characterization of the parallel transportation law associated with the geometric pseudohyperbolic phase of the light ray is given. Later, a principle nature of electric and magnetic field along with the light ray in the pseudohyperbolic space H 2 0 is defined by the geometric invariants. Finally, optical solutions of nonlinear pseudohyperbolic Schrödinger's equations governing the propagation of electromagnetic fields are successfully derived by using the traveling wave hypothesis approach.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New approach for propagated light with optical solitons by optical fiber in pseudohyperbolic space ℍ02

Körpınar

Băleanu

et al. 2021

Math Methods in App Sciences

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“…The nonlocal property of differential equations of arbitrary order is the main advantage over classical differential equations, so it has wide applications as discussed above. Due to the specific characteristic of nonlocality, the physical behavior of a system can be observed in a better way [1–22].…”

Section: Introductionmentioning

confidence: 99%

An efficient numerical approach for fractional multidimensional diffusion equations with exponential memory

Singh

Kumar

Purohıt

et al. 2020

Numerical Methods Partial

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In this article, we suggest a numerical approach based on q‐homotopy analysis Elzaki transform method (q‐HAETM) to solve fractional multidimensional diffusion equations which represents density dynamics in a material undergoing diffusion. We take the noninteger derivative in the Caputo–Fabrizio kind. The proposed method, q‐HAETM is an advanced adaptation in q‐HAM and Elzaki transform method which makes mathematical calculation very effective additionally more accurate. Since, in classical perturbation scheme, the scheme restricted to the small parameter whereas the q‐HAETM is not restricted to the small parameter. By theoretical and numerical evaluation it is observed that q‐HAETM yields an analytical solution in the form of a convergent series. By taking three examples and applying q‐HAETM, the numerical results reveal that the suggested method is straightforward to apply and computationally very effective.

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