The solution of the fractional hyperbolic partial differential equation is obtained by means of the variational iteration method. Our numerical results are compared with those obtained by the modified Gauss elimination method. Our results reveal that the technique introduced here is very effective, convenient, and quite accurate to one-dimensional fractional hyperbolic partial differential equa...

We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method. We use this method for solving Generalized Time-space Fractional Schrödinger equation. The fractional derivative is described in Caputo sense. The proposed scheme finds the solution without any discritization, ...

We study in this paper the existence and approximation of solutions of variational inequalities involving generalized pseudo-contractive mappings in Banach spaces. The convergence analysis of a proposed hybrid iterative method for approximating common zeros or fixed points of a possibly infinitely countable or uncountable family of such operators will be conducted within the conceptual framewor...

Estimating the disparity field between two stereo images is a common task in computer vision, e.g., to determine a dense depth map. Variational methods currently are among the most accurate techniques for dense disparity map reconstruction. In this paper a multi-level adaptive technique is combined with a multigrid approach that allows the variational method to achieve real-time performance (on...

In this paper, we introduce a new system of quasi variational inequalities. The projection technique is used to establish the equivalence between this new system of quasi variational inequalities and the fixed point problem. The fixed point formulation enables us to suggest some parallel projection iterative methods for solving the system of quasi variational inequalities. Convergence analysis ...

In this paper, we introduce and study a new class of generalized mixed quasi-variational-like inequalities. Using the auxiliary principle technique, we construct a new iterative algorithm for finding the approximate solutions of the generalized mixed quasi-variational-like inequality. An existence result of solutions for the generalized mixed quasi-variational-like inequality and the convergenc...

We introduce and consider some new systems of extended general variational inclusions involving six different operators. We establish the equivalence between this system of extended general variational inclusions and the fixed points using the resolvent operators technique. This equivalent formulation is used to suggest and analyze some new iterativemethods for this system of extended general v...

Variational inference is a scalable technique for approximate Bayesian inference. Deriving variational inference algorithms requires tedious model-specific calculations; this makes it di cult for non-experts to use. We propose an automatic variational inference algorithm, automatic di erentiation variational inference ( ); we implement it in Stan (code available), a probabilistic programming sy...