The 2-D Fourier transform has been generalized into the 2-D separable fractional Fourier transform (replaces 1-D Fourier transform by 1-D fractional Fourier transform for each variable) and the 2-D separable canonical transform (further replaces the fractional Fourier transform by canonical transform) in [3]. It also has been generalized into the 2-D unseparable fractional Fourier transform wit...

in this manuscript a new method is introduced for solving fractional differential equations. the fractional derivative is described in the caputo sense. the main idea is to use fractional-order legendre wavelets and operational matrix of fractional-order integration. first the fractional-order legendre wavelets (flws) are presented. then a family of piecewise functions is proposed, based on whi...

in this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (fpdes) in the sense of modified riemann-liouville derivative. with the aid of symbolic computation, we choose the space-time fractional zakharov-kuznetsov-benjamin-bona-mahony (zkbbm) equation in mathematical physics with a source to illustrate the validity a...

This study investigates the use of differential transform method (DTM) for integrating Rössler system fractional order. Preliminary studies integer-order system, with reference to other well-established integration methods, made it possible assess quality and determine optimal parameter values that should be used when a different dynamic characteristics. Bifurcation diagrams obtained show that,...

and Applied Analysis 3 4. Solution by Homotopy Perturbation Sumudu Transform Method (HPSTM) 4.1. Basic Idea of HPSTM. To illustrate the basic idea of this method, we consider a general fractional nonlinear nonhomogeneous partial differential equationwith the initial condition of the form D α t U (x, t) + RU (x, t) + NU (x, t) = g (x, t) , (11) U (x, 0) = f (x) , (12) where Dα t U(x, t) is the C...

When defining a differential operator, one often employs, besides ordinary derivatives, generalized derivatives, which appear in a natural way when considering extensions of differential operators defined on differentiable functions, and weak derivatives, related to the transition to the adjoint operator [9]. Derivatives of fractional and negative orders appear when the differentiation is defin...