In this manuscript, the Laplace Adomian decomposition method (LADM) is presented to solve Newell-Whitehead-Segel equation. The method can be applied to linear and nonlinear problems. Some examples have been carried out in order to illustrate the efficiency and reliability of the method.

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In this work, an incorporated form of Sadik transform and Adomian decomposition method which is called the Sadik decomposition method is presented. The method is applied to solve a system of nonlinear fractional Volterra integro-differential equations in the convolution form. To avoid collecting the noise terms that lead the method to fail for seeking the solution, the proposed method is modified by selecting a suitable initial solution. The obtained results are expressed in the explicit form of a power series with easily computable terms. In addition, illustrative examples are shown to demonstrate the effectiveness of the method.

This article presents the concept of ı ⋆ -continuous multifunctions in ideal topological spaces. Especially, several characterizations of ı ⋆ -continuous multifunctions are investigated. Moreover, the relationships between ı ⋆ -continuity and the other types of continuity for multifunctions are established.

The double integral transform is a robust implementation that is important in handling scientific and engineering problems. Besides its simplicity of use and straightforward application to the issue, the ability to reduce the problems to an algebraic equation that can be easily solved is a substantial advantage of the tool. Among the several integral transforms, the double Sadik transform is acknowledged to be one of the most frequently used in solving differential and integral equations. This work deals with investigating a generalized double integral transform called the double Sadik transform. The proof of the double Sadik transforms for partial fractional derivatives in the Caputo sense is displayed, and the double Sadik transforms method is introduced. The method has been applied to solve the initial boundary value problems for linear space and timefractional telegraph equations. Moreover, the suggested strategy can be used on non-linear problems via an iterative method and a decomposition concept. Some known-solution questions are evaluated with relatively minimal computational cost. The results are represented by utilizing the Mittag-Leffler function and covering the solution of a classical telegraph equation. The obtained exact solutions not only show the accuracy and efficiency of the technique, but also reveal reliability when compared to those obtained using other methods.