In this paper the propagation of harmonic plane waves in a homogeneous anisotropic magneto-piezothermoelastic diffusive body with fractional order derivative is studied. The governing equations for a homogeneous transversely isotropic body in the context of the theory of thermoelasticity with diffusion given by Sherief et al. [1] are considered as a special case. It is found that three types of...

in this paper, we introduce a family of fractional-order chebyshev functions based on the classical chebyshev polynomials. we calculate and derive the operational matrix of derivative of fractional order $gamma$ in the caputo sense using the fractional-order chebyshev functions. this matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

A generalized thermo-elastic diffusion problem in a functionally graded isotropic, unbounded, rotating elastic medium due to a periodically varying heat source in the context of fractional order theory is considered in our present work. The governing equations of the theory for a functionally graded material with GNIII model are established. Analytical solution of the problem is derived in Lapl...

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

The mathematical model of the distribution of deformation-relaxation and heat-mass fields in capillary-porous materials with fractal structure in the process of drying wood is regarded in the article. We used differential equations in partial derivatives of fractional order in description of this model. To describe the creep of wood fractional exponential Rabotnov’s function was used. The numer...

Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...

fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. for that reason, we need a reliable and efficient technique for the solution of fractional differential equations. the aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

In this paper we obtain bounds for the decay rate for solutions to the nonlocal problem ∂tu(t, x) = R n J(x, y)[u(t, y) − u(t, x)]dy. Here we deal with bounded kernels J but with polynomial tails, that is, we assume a lower bound of the form J(x, y) ≥ c1|x − y| −(n+2σ) , for |x − y| > c2. Our estimates takes the form u(t) L q (R n) ≤ Ct − n 2σ (1− 1 q) for t large.