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...

Let D denote the Riemann-Liouville fractional differential operator of order α. Let 1 < α < 2 and 0 < β < α. Define the operator L by L = D − aD where a ∈ R. We give sufficient conditions for the existence of solutions of the nonlinear fractional boundary value problem Lu(t) + f(t, u(t)) = 0, 0 < t < 1, u(0) = 0, u(1) = 0.

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...

Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...

We introduce a concept of a fractional derivatives series and prove that any linear partial differential equation in two independent variables has a fractional derivatives series solution with coefficients from a differentially closed field of zero characteristic. The obtained results are extended from a single equation to D-modules having infinitedimensional space of solutions (i.e., non-holon...

In this paper, variational iteration method (VIM) is applied to solve nonlinear oscillators of fractional order. The time-fractional derivatives are described in the Jumarie’s derivative sense. The application of variational iteration method, developed for differential equations of integer order, is extended to derive explicit analytical solutions of the fractional order nonlinear oscillator’s ...