The aim of this paper is to study a conservative wave equation coupled to a diffusion equation : this coupled system naturally arises in musical acoustics when viscous and thermal effects at the wall of the duct of a wind instrument are taken into account. The resulting equation, known as Webster-Lokshin model, has variable coefficients in space, and a fractional derivative in time. The port-Ha...

This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application t...

Based on the definition of the instantaneous frequency (signal phase derivative) as a local moment of the Wigner distribution, we derive the relationship between the instantaneous frequency and the derivative of the squared modulus of the fractional Fourier transform (fractional Fourier transform power spectrum) with respect to the angle parameter. We show that the angular derivative of the fra...

In the paper, we present a new definition of fractional derivative with a smooth kernel which takes on two different representations for the temporal and spatial variable. The first works on the time variables; thus it is suitable to use the Laplace transform. The second definition is related to the spatial variables, by a non-local fractional derivative, for which it is more convenient to work...

This article presents a rigorous review of the conformable fractional derivative given by J. E. Napoles in [11], studying its classical properties, as differential operator. Likewise, applications are to Physics, specifically free fall bodies and Newton’s law cooling.

In this article, we consider the multi-point boundary-value problem for nonlinear fractional differential equations with p-Laplacian operator: D 0+ φp(D α 0+ u(t)) = f(t, u(t), Dα−2 0+ u(t), Dα−1 0+ u(t), D 0+ u(t)), t ∈ (0, 1), u(0) = u′(0) = D 0+ u(0) = 0, Dα−1 0+ u(1) = m X i=1 σiD α−1 0+ u(ηi), where 2 < α ≤ 3, 0 < β ≤ 1, 3 < α+β ≤ 4, Pm i=1 σi = 1, D α 0+ is the standard Riemann-Liouville ...

In the sense of a conformable fractional operator, we consider generalized fractional–stochastic nonlinear wave equation (GFSNWE). This may be used to depict several physical phenomena occurring in liquid containing gas bubbles. The analytical solutions GFSNWE are obtained by using F-expansion and Jacobi elliptic function methods with Riccati equation. Due presence noise derivative, some that w...

n this paper, at first the  concept of caputo fractionalderivative is generalized on time scales. then the fractional orderdifferential equations are introduced on time scales. finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.