By considering the initial and boundary conditions corresponding to parallel subsurface drains, the linear form of a one-dimensional fractional Boussinesq equation was solved and an analytical mathematical model was developed ...

In this article, we develop an effective numerical method to achieve the numerical solutions of nonlinear fractional Riccati differential equations. We found the operational matrix within the linear B-spline functions. By ...

Recently Caputo and Fabrizio suggested new definition of fractional derivative that the new kernel has no singularity. In this paper, an analytical method for solving Riccati differential equation with a new fractional ...

In recent years, many approaches have been utilized for finding the exact solutions of nonlinear partial differential equations. One such method is known as the first integral method and was proposed by Feng. In this paper, ...

The porous medium which groundwater flows in is heterogeneous at all scales. This complicates the simulation of groundwater flow. Fractional derivatives, because of their non-locality property, can reduce the scale effects ...

In this paper the fractional sub-equation method is used to construct exact solutions of the fractional generalized reaction Duffing model and nonlinear fractional Sharma-Tasso-Olver equation.The fractional derivative is ...

In this study, the homotopy analysis method is used for solving the Abel differential equation with fractional order within the Caputo sense. Stabilityand convergence of the proposed approach is investigated. The numerical ...

Discrete fractional calculus (DFC) is continuously spreading in the engineering practice, neural networks, chaotic maps, and image encryption, which is appropriately assumed for discrete-time modelling in continuum problems. ...

In our manuscript we suggest an approach to obtain the solutions of the fractional differential equations(FDEs). We found the operational matrix within the linear B-spline functions. In this way the investigated equations ...

We investigate sufficient conditions for existence and uniqueness of solutions for a coupled system of fractional order hybrid differential equations (HDEs) with multi-point hybrid boundary conditions given by D-omeg ...