Fractional order theory of thermo-viscoelasticity and application

Sherief, Hany H.; Elhagary, M. A.

doi:10.1007/s11043-019-09415-2

Cited by 36 publications

(12 citation statements)

References 29 publications

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“…[1][2][3][4] Also fractional order has a wide range of applications in many fields such as quantum mechanics, chemical physics, dynamics, power networks, viscoelasticity, and medicine. [5][6][7][8][9] In the article, 10 the authors studied the dynamics of tuberculosis using a fractional order model. In the article, 11 the authors used Caputo derivatives to generalize the mathematical model of hepatitis B virus and used the definition of fractional stability to investigate the model results.…”

Section: Introductionmentioning

confidence: 99%

“…Fractional order calculus has become a powerful tool for the study of fractional order differential equations, fractal functions, and so forth, and is widely used in the study of fractal geometry, fractal functions, fractal partial differential equations, function spaces, and other fields 1‐4 . Also fractional order has a wide range of applications in many fields such as quantum mechanics, chemical physics, dynamics, power networks, viscoelasticity, and medicine 5–9 …”

Section: Introductionmentioning

confidence: 99%

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Convergence analysis of Riemann‐Liouville fractional neural network

Dong

Liao

et al. 2022

Math Methods in App Sciences

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Many fractional order calculus researchers believe that fractional order calculus is a good way to solve information processing as well as certain physical system modeling problems. In the training of neural networks, there is the problem of long convergence time. In order to shorten the convergence time of the network, an R-L gradient descent method is proposed in this study. The article begins with a theoretical proof of the convergence of fractional order derivatives using function approximation and interpolation inequality theorems. Finally, through multiple simulations, it can be obtained that the fractional-order neural network can maintain a higher accuracy rate compared with the integer-order neural network, and also can well solve the problem of longer convergence time of the neural network. The convergence time can be reduced by nearly 10% compared to the integer order.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Convergence analysis of Riemann‐Liouville fractional neural network

Dong

Liao

et al. 2022

Math Methods in App Sciences

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“…Some contributions to this theory are in previous works. [24][25][26] Sherief and El-Hagary 27 derived a new model of thermoviscoelasticity using the methodology of FC.…”

Section: Introductionmentioning

confidence: 99%

2D hereditary thermoelastic application of a thick plate under axisymmetric temperature distribution

Sherief

El-Latief

Fayik

2021

Math Methods in App Sciences

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In this work, we present a new theory of generalized fractional hereditary thermoelasticity associated with Mittag–Leffler relaxation function. We analyze a two‐dimensional problem of a thick plate of hereditary thermoelastic. The lower and upper surfaces of the plate are assumed to be traction free and subjected to a given axisymmetric temperature distribution. Direct approach together with Laplace and Hankel transform techniques is employed to obtain the solution in the transformed domain. Hankel transforms are inverted analytically while a numerical method is used for the Laplace transform inversion. The distributions of different fields like temperature, displacement, and stresses have been computed and shown graphically.

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“…They used a modified heat conduction law to introduce the generalized theory of thermoelasticity. This theory was extended to include different effects by Sherief et al [3–9]. Some contributions to the subject of these theories can be found elsewhere [10–14].…”

Section: Introductionmentioning

confidence: 99%

Exact solution of a 2D problem of thermoelasticity without energy dissipation for an infinitely long cylinder

Sherief

Elhagary

2021

Mathematics and Mechanics of Solids

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We consider a 2D problem of a circular cylinder that is infinitely long and whose external surface is free from outside effects and acted upon by an asymmetrical temperature distribution that is harmonic in time. The problem is within the context of the theory of thermoelasticity without energy dissipation. The exact solution is obtained by a direct approach. The results are represented graphically and discussed.

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Fractional order theory of thermo-viscoelasticity and application

Cited by 36 publications

References 29 publications

Convergence analysis of Riemann‐Liouville fractional neural network

Convergence analysis of Riemann‐Liouville fractional neural network

2D hereditary thermoelastic application of a thick plate under axisymmetric temperature distribution

Exact solution of a 2D problem of thermoelasticity without energy dissipation for an infinitely long cylinder

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