Local fractional variational iteration and decomposition methods for wave equation on cantor sets within local fractional operators

We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

Controllability results for impulsive mixed type functional integro-differential evolution equations with nonlocal conditions

In this paper, we establish the controllability for a class of abstract impulsive mixed-type functional integro-differential equations with finite delay in a Banach space. Some sufficient conditions for controllability are obtained by using the Mönch fixed point theorem via measures of noncompactness and semigroup theory. Particularly, we do not assume the compactness of the evolution system. An example is given to illustrate the effectiveness of our results.

Shear modulus and strength of an acrylic adhesive by the notched plate shear method (Arcan) and the thick adherend shear test (TAST)

In this work, the shear modulus and strength of the acrylic adhesive 3M® DP 8005 was evaluated by two different methods: the Thick Adherend Shear Test (TAST) and the Notched Plate Shear Method (Arcan). However, TAST standards advise the use of a special extensometer attached to the specimen, which requires a very experienced technician. In the present study, the adhesive shear displacement for the TAST was measured using an optical technique, and also with a conventional inductive extensometer of 25 mm used for tensile tests. This allowed for an assessment of suitability of using a conventional extensometer to measure this parameter. Since the results obtained by the two techniques are identical, it can be concluded that using a conventional extensometer is a valid option to obtain the shear modulus for the particular adhesive used. In the Arcan tests, the adhesive shear displacement was only measured using the optical technique. This work also aimed the comparison of shear modulus and strength obtained by the TAST and Arcan test methods.

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

Nonlinear Dynamics for Local Fractional Burgers Equation Arising in Fractal Flow

The local fractional Burgers’ equation (LFBE) is investigated from the point of view of local fractional conservation laws envisaging a nonlinear local fractional transport equation with a linear non-differentiable diffusion term. The local fractional derivative transformations and the LFBE conversion to a linear local fractional diffusion equation are analyzed.