Haar wavelets for the solution of fractional integral equations are applied. Fractional Vol-terra and Fredholm integral equations are considered. The proposed method also is used for analysing fractional harmonic vibrations. The efficiency of the method is demonstrated by three numerical examples. Although the conception of the fractional derivatives was introduced already in the middle of the ...

Based on cascading nonlinear interactions of second harmonic generation (SHG) and difference frequency generation (DFG), we present a novel scheme to control the group velocity of femtosecond pulse in MgO doped periodically poled lithium niobate crystal. Group velocity of tunable signal pulse can be controlled by another pump beam within a wide bandwidth of 180nm. Fractional advancement of 2.4 ...

A new technique to study the telegraph equation, mostly familiar as damped wave equation is introduced in this study. This phenomenon rising electromagnetic influences and production of electric signals. The proposed called He-Fractional Laplace with help Homotopy perturbation utilized found exact nearly approximated results differential model numerical example or article. most unique term that...

Analysis of the free and forced vibration responses beams is one most critical problems to be examined in design step these structural members. The finite-element method which solves boundary value can applied efficiently problems. In this study, natural frequency damped undamped transient analyses pinned-pinned are investigated. well-known software packages, ANSYS SAP2000, used. 2-D elastic be...

In this article, we study the nonexistence of global solutions to a semi-linear structurally damped wave equation with nonlinear memory in R n $\mathbb {R}^n$ for any space dimension ≥ 1 $n\ge 1$ and initial arbitrarily data being subject positivity assumption. We intend apply method test function establish blow-up results overcome some difficulties as well caused by well-known fractional Lapla...

In this paper, we give a review of the tensor method for treating the propagation of scalar and electromagnetic Gaussian Schell-model (GSM) beams. Partially coherent complex curvature tensor is introduced to describe a scalar astigmatic partially coherent GSM beam with twisted phase (i.e., twisted anisotropic GSM beam). A tensor ABCD law for treating the propagation of scalar twisted anisotropi...

We introduce an analytical procedure to construct an optical beam with an arbitrary value of orbital-angular momentum (OAM) by keeping the flexibility of shaping its transverse intensity distribution without changing its OAM. We apply the general theory of fractional differential operators in Fourier domain to derive general expressions for the OAM content in the beam and find the relevant para...

We introduce the generalized Helmholtz-Gauss (gHzG) beam and analyze its propagation through optical systems described by ABCD matrices with real and complex elements. The transverse mathematical structure of the gHzG beam is form invariant under paraxial transformations and reduces to those of ordinary HzG and modified HzG beams as special cases. We derive a closed-form expression for the frac...

We consider a compressible fluid structure interaction model in 2D channel with simplified expression of the net force acting on appearing at boundary. Concerning we will damped Euler-Bernoulli beam located portion In present article establish an observability inequality for adjoint linearized problem under consideration which principle is equivalent null controllability system. As corollary de...