A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple (L (2)(Ω)(2)) space replacing the complex H(div; Ω) space. Some a priori error estimates in L...

In this present work, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the direct algebraic method are employed for constructing the exact complex solutions of non-linear time-fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. Reference to this paper should be made as follows: Taghiz...

In this study, solutions of time-space fractional partial differential equations(FPDEs) are obtained by utilizing the Shehu transform iterative method. The utilityof technique is shown getting numerical to a large number FPDEs.

In this paper the authors prove existence, uniqueness and approximation of the solutions for initial value problems of nonlinear fractional differential equations with nonlocal conditions, using the operator theoretic technique in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid fixed point theorem of Dhage (2014) in a partia...