On the explicit solutions of fractional Bagley-Torvik equation arises in engineering

Pınar, Zehra

doi:10.11121/ijocta.01.2019.00638

Cited by 12 publications

(8 citation statements)

References 49 publications

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“…The fractional kinds of derivatives represent the physical network dynamics, a rigid plate based on the Newtonian fluid, and the frequency-dependent systems of the damping properties [1][2][3][4]. The numerical, approximate and analytical form of the FBTMM has been performed by many scientists and reported in [6][7][8][9][10]. While few other utmost deterministic and stochastic numerical schemes [11][12][13][14][15][16][17][18][19] are listed in Table 1 in terms of novel methodology exploited for the solutions, publication year, and necessary remarks to highlight their significance in the reported literature for FBTMM.…”

Section: Introductionmentioning

confidence: 99%

Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model

et al. 2022

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This study is to introduce a novel design and implementation of a neuro-swarming computational numerical procedure for numerical treatment of the fractional Bagley–Torvik mathematical model (FBTMM). The optimization procedures based on the global search with particle swarm optimization (PSO) and local search via active-set approach (ASA), while Mayer wavelet kernel-based activation function used in neural network (MWNNs) modeling, i.e., MWNN-PSOASA, to solve the FBTMM. The efficiency of the proposed stochastic solver MWNN-GAASA is utilized to solve three different variants based on the fractional order of the FBTMM. For the meticulousness of the stochastic solver MWNN-PSOASA, the obtained and exact solutions are compared for each variant of the FBTMM with reasonable accuracy. For the reliability of the stochastic solver MWNN-PSOASA, the statistical investigations are provided based on the stability, robustness, accuracy and convergence metrics.

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Section: Introductionmentioning

confidence: 99%

Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model

et al. 2022

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“…The exact solutions and numerical solutions of the nonlinear fractional partial differential equations play an important role in physical science and in engineering fields such as viscoelasticity, fluid mechanics, acoustics, electromagnetism, diffusion, analytical chemistry, control theory, biology, and so on [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Consequently, there have been attempts to develop new methods to obtain approximate analytical solutions which converge to exact solutions.…”

Section: Introductionmentioning

confidence: 99%

A new modification of the reduced differential transform method for nonlinear fractional partial differential equations

Khalouta¹,

Kadem²

2020

J. Appl. Math. Comput. Mech.

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The objective of this study is to present a new modification of the reduced differential transform method (MRDTM) to find an approximate analytical solution of a certain class of nonlinear fractional partial differential equations in particular, nonlinear time-fractional wave-like equations with variable coefficients. This method is a combination of two different methods: the Shehu transform method and the reduced differential transform method. The advantage of the MRDTM is to find the solution without discretization, linearization or restrictive assumptions. Three different examples are presented to demonstrate the applicability and effectiveness of the MRDTM. The numerical results show that the proposed modification is very effective and simple for solving nonlinear fractional partial differential equations.

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“…The nonlinear partial differential equations (NPDEs) have so many essential applications in various fields of engineering and science, such as heat transfer, fluid mechanics, chemistry, thermodynamic, physics, micro electro-mechanic system, etc. These equations have been being employed to describe many complex phenomena [1][2][3][4][5][6][7][8][9][10]. So, finding the exact and numerical solutions of these model have been being attracted the attention of many researchers in various branches of science.…”

Section: Introductionmentioning

confidence: 99%

Abundant new computational wave solutions of the GM-DP-CH equation via two modified recent computational schemes

Khater

Inc

Attia

et al. 2020

Journal of Taibah University for Science

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This work employs two new modified computational schemes to find the exact travelling and solitary wave solutions of the general modified Degasperis-Procesi Camassa-Holm (DP CH) equation that is used to illustrate the dynamical behaviour of shallow water. These schemes are the modified exponential expansion and the modified Khater methods that are used to formulate the computational solutions in various formulas such as trigonometric, hyperbolic, exponential functions. The obtained solutions are explained and figured out their substantial contributions in three different types of sketches (three, two-dimensional, and contour plots).

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On the explicit solutions of fractional Bagley-Torvik equation arises in engineering

Cited by 12 publications

References 49 publications

Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model

Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model

A new modification of the reduced differential transform method for nonlinear fractional partial differential equations

Abundant new computational wave solutions of the GM-DP-CH equation via two modified recent computational schemes

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