Although Elzaki transform is stronger than Sumudu and Laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. In this paper, a method is introduced to find that a differential equation by Elzaki transform can be ‎solved?‎

In this paper, we apply the local fractional Laplace transform method (or Yang-Laplace transform) on Volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative operators. This approach provides us with a convenient way to find a solution ...

in this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. in additional, the least-squares method is adopted to nd the solution. to regularize the resultant ill-conditioned linear system ofequations, we apply the tikhonov regularization method to obtain the stablenumerical approximation to the solution. some numerical experiments con- rm the utility of...

Abstract: Motivated by statistical mechanics contexts, we study the properties of the q-Laplace transform, which is an extension of the well-known Laplace transform. In many circumstances, the kernel function to evaluate certain integral forms has been studied. In this article, we establish relationships between q-exponential and other well-known functional forms, such as Mittag–Leffler functio...

in this paper, inverse laplace transform method is applied to analytical solution of the fractional sturm-liouville problems. the method introduces a powerful tool for solving the eigenvalues of the fractional sturm-liouville problems. the results  how that the simplicity and efficiency of this method.

Abstract. In this paper a reliable algorithm for the iterative Laplace transform method (ILTM) is presented. ILTM is a combination of Laplace transform method and Iterative method to solve spaceand timefractional telegraph equations. The fractional derivatives are considered in Caputo sense. Closed form analytical expressions are derived in terms of the Mittag-Leffler functions. An illustrative...

In this paper, a Laplace transform decomposition algorithm (LTDA) is proposed to solve the Riccati equation. Comparisons are made among the homotopy perturbation method (HPM), the Adomian decomposition method (ADM) and the proposed method. It is shown that the homotopy perturbation method with a specific convex homotopy is equivalent to the Adomian decomposition method and the Laplace transform...

Effects of the uniform transverse magnetic field on the transient free convective flows of a nanofluid with generalized thermal transport between two vertical parallel plates have been analyzed. The fluid temperature is described by a time-fractional differential equation with Caputo derivatives. Closed form of the temperature field is obtained by using the Laplace transform and fractional deri...