During the past years, a wide range of distinct approaches has been exerted to solve the nonlinear Fractional differential equations (NLFDEs). In this paper, the invariant subspace method (ISM) in conjunction with the Fractional Sumudu’ s transform (FST) in the conformable context is formally adopted to deal with a nonlinear conformable time-Fractional dispersive equation of the fifth-order. As an outcome, a new exact solution of the model is procured, corroborating the exceptional performance of the hybrid scheme.

In this paper, we apply Fractional complex transform to convert the Fractional nonlinear Schrodinger equations to the nonlinear Schrodinger equations.

We expand a new generalization of the two-dimensional differential trans-form method. The new generalization is based on the two-dimensional differ-ential transform method, Fractional power series expansions, and conformable Fractional derivative. We use the new method for solving a nonlinear con-formable Fractional partial differential equation and a system of conformable Fractional partial differential equation. Finally, numerical examples are pre-sented to illustrate the preciseness and effectiveness of the new technique.

The performance of Orthogonal Frequency Division Multiple Access (OFDMA) system degrades significantly in doubly dispersive channels. This is due to the fact that exponential sub-carriers do not match the singular functions of this type of channels. To solve this problem, we develop a system whose sub-carriers are chirp functions. This is equivalent to exploiting Fractional Fourier transform (FrFT) instead of Fourier transform (FT) in the structure of the aforementioned transmission scheme. We name the new system FrFT-OFDMA. The optimal angle of Fractional Fourier transform for each user depends on its channel parameters. Thus, the angles of transform for different users are not necessarily identical. This destroys the orthogonality of users and generates Multi-User Interference (MUI). By analyzing MUI, we introduce quasi-orthogonality conditions where interference is negligible despite different angles of transform. For non-orthogonal users, we propose a method to mitigate MUI. We present the efficiency of this method through comparative performance evaluation of the conventional system based on FT and the new system based on FrFT. We show that our proposed transmission scheme outperforms the traditional OFDMA system significantly in doubly dispersive channels and channels impaired by frequency offset.

In this paper, an iterative method for obtaining the numerical solutions of Fractional partialdifferential equations (FPDEs) is introduced. This method is based on the combination of the differentialtransformation method (DTM) with Fractional linear multistep methods (FLMM). The proposed methodhas a very low computational cost, with the help of which partial Fractional differential equations areconverted into a system of ordinary differential equations. Then the resulting equations are solved with highaccuracy by applying Fractional linear multi-step methods such as Fractional Euler The series of solutionsobtained in the differential transformation method has a slow convergence speed in large regions. In thisstudy, by combining the mentioned method with linear multi-step methods, this shortcoming is solved.Numerical results show that the obtained solutions. They are in good agreement with the exact solution ofthe Fractional differential equation. The obtained results confirm the proven stability and accuracy of themethod.

In this paper, new analytical solutions for a class of conformable Fractional differential equations (CFDEs) and some more results about Laplace transform introduced by Abdeljawad are investigated. The Laplace transform method is developed to get the exact solution of CFDEs. The aim of this paper is to convert the CFDEs into ordinary differential equations (ODEs), this is done by using the Fractional Laplace transform of (α,+ β, ) order.