This manuscript suggests an efficient scheme to find an approach for a class of differential equations arsing in the quantum calculus. The present scheme considers the solution in the form of a truncated Taylor series near zero with unknown coefficients. Then, by placing this approach into the problem and collocating the relation which is obtained at some nodes, a system of algebraic equations is achieved. The solution of this algebraic system is the unknown coefficients of the series. The ability of present method is examined by some examples.

This study presents the approximate solutions of a system of Fractional Integro-Differential Equations (FIDEs) with least squares collocation Chebyshev technique. The technique reduce the problem to system of linear algebraic equations and then solved. The applicability of this method has been demonstrated by numerical examples. Numerical results show that the method is easy to implement and compares favorably with the exact results.

Analysis of complex one-dimensional photonic systems is a challenge to the scientific community. To solve such a problem in the past computational techniques have been deployed. Transfer matrix or so-called characteristics matrix is one of the widely used methods acceptable for multilayered systems. The convectional transfer matrix method has some drawbacks to solving an annular type multilayered system. This paper presents the transfer matrix method to investigate the electromagnetic wave propagation in the annular multilayered photonic structures.

In this study, the Fan sub-equation method is applied to study exact solutions of complexnonlinear time fractional Maccari system. Using this method, we obtain various solutions which thoseare useful t to understand better the concepts of the complicated physical phenomena. This method isstraightforward, and it can be used to many nonlinear equations.

The fractional variational iteration technique (FVIM), a dependable semi-analytic approach for solving multi-dimensional Navier-Stokes equations, is explained in this article. The accuracy, efficiency, and convergence of the provided approach are tested using a variety of demonstrative instances.

We solve the Schrodinger equation for the combination of Kratzer and Modified Eckart potential by using an approximation to the centrifugal term. Analytical expressions of the energy and the corresponding eigenfunctions have been obtained by using the parametric Nikiforov-Uvarov method. Special cases of the potential are discussed. In addition, numerical results of the energy are computed. Furthermore, it is reported that the energy E and the quantum numbers n and l are inversely proportional to each other.