In this paper, a fractional complex transform (FCT) is used to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and subsequently Reduced Differential Transform Method (RDTM) is applied on the transformed system of linear and nonlinear time-fractional PDEs. The results so obtained are re-stated by making use of inverse t...

In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation m...

Fractional derivatives have been around for centuries [22, 26] but recently they have found new applications in physics [2, 6, 7, 9, 15, 18, 19, 29], hydrology [1, 4, 5, 10, 14, 28], and finance [24, 25, 27]. Analytical solutions of ordinary fractional differential equations [22, 23] and partial fractional differential equations [8, 16] are now available in some special cases. But the solution ...

a method for solving a class of weakly singular volterra integral equations is given by using the fractional differential transform method. the approximate solution of these equa­tions is calculated in the form of a finite series with easily computable terms. while in some examples this series solution increased up to the exact closed solution, in some other examples, we can see the accuracy an...

In this paper, Bernoulli wavelets are presented for solving (approximately) fractional differential equations in a large interval. Bernoulli wavelets operational matrix of fractional order integration is derived and utilized to reduce the fractional differential equations to system of algebraic equations. Numerical examples are carried out for various types of problems, including fractional Van...

In this letter we develop a new generalization of the two-dimensional differential transform method that will extend the application of the method to linear partial differential equations with spaceand time-fractional derivatives. The new generalization is based on the two-dimensional differential transform method, generalized Taylor’s formula and Caputo fractional derivative. Several illustrat...

‎in this paper‎, ‎a spectral tau method for solving fractional riccati‎ ‎differential equations is considered‎. ‎this technique describes‎ ‎converting of a given fractional riccati differential equation to a‎ ‎system of nonlinear algebraic equations by using some simple‎ ‎matrices‎. ‎we use fractional derivatives in the caputo form‎. ‎convergence analysis of the proposed method is given an...

Fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. For that reason, we need a reliable and efficient technique for the solution of fractional differential equations. The aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...