Fractional derivatives on cosmic scales

Учайкин, В. В.; Sibatov, Renat T.

doi:10.1016/j.chaos.2017.04.023

Cited by 7 publications

(2 citation statements)

References 65 publications

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“…FDEs have been used extensively to model many well known physical phenomena. Just to mention a few, FDEs are used to model different processes in viscoelasticity [9], image processing [10], combustion [11], dynamics and control theory [12], motion of Newtonian fluid [13], earth science dynamics [14], cosmology [15], financial economics [16], biological processes [17].…”

Section: Introductionmentioning

confidence: 99%

Inverse problem for recovery of temporal component of source term for multi-term time fractional parabolic equation with nonlocal boundary datum

Ali¹,

Aziz²

2022

Preprint

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Inverse problem for multi-term fractional parabolic equation in two dimensional space, involving m + 1 Caputo fractional derivatives in time, is investigated. Presence of nonlocal boundary conditions leads to a non-self-adjoint spectral problem. A bi-orthogonal system of functions is used to construct the solution that involves double infinite series. Properties of multinomial Mittag-Leffler function and eigenfunctions are used to prove the classical nature of the solution under certain regularity conditions on the given datum.

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Section: Introductionmentioning

confidence: 99%

Inverse problem for recovery of temporal component of source term for multi-term time fractional parabolic equation with nonlocal boundary datum

Ali¹,

Aziz²

2022

Preprint

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“…Uchaikin and Sibatov [23] studied fractional derivatives on cosmic scales. The numerical calculation results demonstrated in this paper do speak well for the NoRDmodel as compared with the traditional one based on integer-order operators.…”

Section: Introductionmentioning

confidence: 99%

Application of Local Fractional Homotopy Perturbation Method in Physical Problems

Habibi

Zohre

2020

Advances in Mathematical Physics

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Nonlinear phenomena have important effects on applied mathematics, physics, and issues related to engineering. Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. The perturbation method is a wave equation solution using HPM compared with the Fourier series method, and both methods results are good agreement. The percentage of error of ux,t with α=1 and 0.33, t =0.1 sec, between the present research and Yong-Ju Yang study for x≥0.6 is less than 10. Also, the % error for x≥0.5 in α=1 and 0.33, t =0.3 sec, is less than 5, whereas for α=1 and 0.33, t =0.8 and 0.7 sec, the % error for x≥0.4 is less than 8.

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Anomalous Diffusion Equations with Multiplicative Acceleration

Saenko

2018

J. Exp. Theor. Phys.

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Fractional derivatives on cosmic scales

Cited by 7 publications

References 65 publications

Inverse problem for recovery of temporal component of source term for multi-term time fractional parabolic equation with nonlocal boundary datum

Inverse problem for recovery of temporal component of source term for multi-term time fractional parabolic equation with nonlocal boundary datum

Application of Local Fractional Homotopy Perturbation Method in Physical Problems

Anomalous Diffusion Equations with Multiplicative Acceleration

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