Fractional Differential Equations

Cours d'economie politique

Integral transforms (Laplace, Fourier and Mellin) are introduced with their properties, the relationship between these transforms was discussed and some important applications in physics and engineering were given. ااااااا دقل مت ضارعتسإ ةساردو ل ةيلماكتلا تليوحتلا لك ، سلبل تلوحت نم روف ي ر نيليمو عم ةشقانم كلذكو ،اهنم لك صاوخ و صئاصخ ةقلعلا ةشقانم مت هذه نيب طبرلاو و ،تليوحتلا مت ميدقت تاقيبطتلا ضعب تليوحتلا هذهل ةمهملا يف تلاجم ءايزيفلا ةسدنهلاو.

Integral transforms and their applications

Thank you very much for downloading thermal stresses advanced theory and applications. As you may know, people have look hundreds times for their chosen novels like this thermal stresses advanced theory and applications, but end up in infectious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they juggled with some malicious virus inside their desktop computer.

Thermal Stresses Advanced Theory And Applications

This work uses the “fractional order bio-heat model” (Fob) model of heat conduction to offer a new interpretation to study the thermal damages in a skin tissue caused by laser irradiation. The influences of fractional order and the thermal relaxation time parameters on the temperature of skin tissue and the resulting thermal damage are studied. In the Laplace domain, the analytical solutions of temperature are obtained. Using the equation of Arrhenius, the resulting thermal injury to the tissues is assessed by the denatured protein ranges. The numerical results of the thermal damages and temperature are presented graphically. A parametric analysis is dedicated to the identifications of suitable procedures for the selection of significant design variables to achieve an effective thermal in the therapy of hyperthermia.

https://www.mdpi.com/2073-8994/12/4/602/pdf

The Effect of Fractional Time Derivative of Bioheat Model in Skin Tissue Induced to Laser Irradiation

This article highlights on the study of coupled plasma, thermal and elastic waves within an orthotropic infinite semiconducting medium in context of photothermal transport process having a spherica...

Photo-thermo-elastic wave propagation in an orthotropic semiconductor with a spherical cavity and memory responses

In this paper, a new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of heat conduction with fractional orders. The two-temperature Lord–Shulman (2TLS) model and two-temperature Green–Naghdi (2TGN) models of thermoelasticity are combined into a unified formulation using the unified parameters. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain which is then solved by using a state-space approach. The inversions of Laplace transforms are computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to estimate the effects of the temperature discrepancy and the fractional order parameter.

Fractional order two-temperature thermoelasticity with finite wave speed

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of magneto-thermoelasticity to investigate the transient phenomena for a fibre-reinforced thick plate having a heat source in the context of three-phase-lag model of generalized thermoelasticity, which is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. The upper surface of the plate is free of traction having a prescribed surface temperature while the lower surface rests in a rigid foundation and is thermally insulated. Employing Laplace and Fourier transforms as tools, the problem has been solved analytically in the transformed domain. The inversion of the Fourier transform is carried out using suitable numerical techniques while the numerical inversion of Laplace transform is done incorporating a method on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Excellent predictive capability is demonstrated due to the presence of memory dependent derivative, magnetic field and reinforcement also.

Modeling of memory-dependent derivative in a fibre-reinforced plate

This paper aims at studying the thermo-viscoelastic interaction in a functionally graded, infinite, Kelvin–Voigt-type viscoelastic, thermally conducting medium due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, Green–Naghdi model II (i.e. the model which predicts thermoelasticity without energy dissipation) and Green–Naghdi model III (i.e. the model which predicts thermoelasticity with energy dissipation) are employed to study thermomechanical coupling, thermal and mechanical relaxation effects. In the absence of mechanical relaxations (viscous effect), the results for various generalised theories of thermoelasticity may be obtained as particular cases. The governing equations are expressed in Laplace–Fourier double transform domain and are solved in that domain. The inversion of the Fourier transform is carried out using residual calculus, where the poles of the integrand are obtained numerically in the complex domain by using Laguerre’s method and the inversio...

/pdf/thermoelastic-interaction-in-a-viscoelastic-functionally-48fwy6wjoi.pdf

Thermoelastic interaction in a viscoelastic functionally graded half-space under three-phase-lag model

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for a piezoelastic half-space due to the influence of a magnetic field in the context of the dual-phase-lag model of generalized thermoelasticity, which is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. The bounding plane of the medium is assumed to be stress free and subjected to a thermal shock. Employing the Laplace transform as a tool, the problem is transformed to the space domain, where the solution in the space–time domain is achieved by applying a suitable numerical technique based on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory are constructed. Excellent predictive capability is demonstrated due to the presence of electric field, memory-dependent derivative and magnetic field.

Abhik Sur

Papers

Photo-thermo-elastic wave propagation in an orthotropic semiconductor with a spherical cavity and memory responses

Fractional order two-temperature thermoelasticity with finite wave speed

Modeling of memory-dependent derivative in a fibre-reinforced plate

Thermoelastic interaction in a viscoelastic functionally graded half-space under three-phase-lag model

Transient response in a piezoelastic medium due to the influence of magnetic field with memory-dependent derivative