The method of monotone iterative technique together with coupled lower and upper solutions is employed to prove the existence of coupled extremal solutions when the forcing function is the sum of an increasing and decreasing functions. This is referred to as generalized monotone method. This will include the usual monotone method results as special cases. Further using uniqueness condition uniq...

Impulsive differential equations are a basic tool for studying evolution processes of real life phenomena that are subjected to sudden changes at certain instants. In view of multiple applications of the impulsive differential equations, it is necessary to develop the methods for their solvability. Unfortunately, a comparatively small class of impulsive differential equations can be solved anal...

We introduce and study a new class of nonlinear general A-monotone operator equations with multivalued operator. By using Alber’s inequalities, Nalder’s results, and the new proximal mapping technique, we construct some new perturbed iterative algorithms with mixed errors for solving the nonlinear general A-monotone operator equations and study the approximationsolvability of the nonlinear oper...

In this paper, we apply our proposed early parallel adaptive computing methodology for numerical solution of semiconductor device equations with triangular meshing technique. This novel simulation based on adaptive triangular mesh, finite volume, monotone iterative, and a posteriori error estimation methods, is developed and successfully implemented on a Linux-cluster with message passing inter...

The main aim of the paper is to present an algorithm solve approximately initial value problems for a scalar non-linear fractional differential equation with generalized proportional derivative on finite interval. condition connected one sided Lipschitz right hand side part given equation. An iterative scheme, based appropriately defined mild lower and upper solutions, provided. Two monotone se...

We investigate the initial value problem for a class of fractional evolution equations in a Banach space. Under some monotone conditions and noncompactness measure conditions of the nonlinearity, the well-known monotone iterative technique is then extended for fractional evolution equations which provides computable monotone sequences that converge to the extremal solutions in a sector generate...