In this article, we solve numerically the linear and non-linear fractional initial value problems of multiple orders by developing a numerical method that is based on the decomposition algorithm coupled with the operational ...

In this paper, a computational approach based on the operational matrices in conjunction with orthogonal shifted Legendre polynomials (OSLPs) is designed to solve numerically the multi-order partial differential equations ...

Many numerical methods have been developed for nonlinear fractional integro-differential Volterra's population model (FVPG). In these methods, to approximate a function on a particular interval, only a restricted number ...

In this paper, we proposed a new fractional derivative operator in which the generalized cardinal sine function is used as a non-singular analytic kernel. In addition, we provided the corresponding fractional integral ...

The focus of this work is to construct a pseudo-operational Jacobi collocation scheme for numerically solving the Caputo variable-order time-fractional diffusion-type equations with applications in applied sciences. Modeling ...

In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based ...

The authors' concern of the present paper is to conduct a systematic study on a time-fractional nonlinear water wave equation which is an evolutionary version of the Boussinesq system. The study goes on by adopting a new ...

This research focus on the determination of the numerical solution for the mathematical model of Fokker-Planck equations utilizing a new method, in which Sumudu transformation and homotopy analysis method (SHAM) are used ...

This paper deals with a mixed-order Caputo fractional system with nonlocal integral boundary conditions. This study can be considered as an extension of previous studies, since the orders of the equations lie on different ...

The definition, properties and applications of the Sumudu transform to ordinary differential equations are described in [1-3]. In this manuscript we derive the formulae for the Sumudu and double Sumudu transforms of ordinary ...