In this paper, we introduce $rho$-altering $J$-type mappings in modular spaces. We prove some fixed point theorems for $rho$-altering and $rho$-altering $J$-type mappings in modular spaces. We also furnish illustrative examples to express relationship between these mappings. As a consequence, the results are applied to the existence of solution of an integral equation arising from an ODE ...

A laminar, two dimensional, steady boundary layer Newtonian conducting fluid flow passes over a permeable shrinking sheet in the presence of a uniform magnetic field is investigated. The governing equations have converted to ordinary nonlinear differential equations (ODE) by using appropriate similarity transformations. The main idea is to transform ODE with infinite boundary condition into oth...

This work investigates the performance of Differential Evolution (DE) and its opposition-based version (ODE) on large scale optimization problems. Opposition-based differential evolution (ODE) has been proposed based on DE; it employs opposition-based population initialization and generation jumping to accelerate convergence speed. ODE shows promising results in terms of convergence rate, robus...

We suggest an approach for description of integrable cases of the Abel equations using the procedure of increasing the order and equivalence transformations for the induced secondorder equations. A diversity of methods were developed to date for finding solutions of nonlinear ordinary differential equations (ODE). Everybody who encounters integration of a particular ODE uses, as a rule, the acc...

Nicotinic acetylcholine receptors (nAChRs) of parasitic nematodes are required for body movement and are targets of important "classical" anthelmintics like levamisole and pyrantel, as well as "novel" anthelmintics like tribendimidine and derquantel. Four biophysical subtypes of nAChR have been observed electrophysiologically in body muscle of the nematode parasite Oesophagostomum dentatum, but...

Ordinary differential equation (ODE) models, e.g. the susceptible-infected-recovered model, are widely used in engineering, ecology, and epidemiology. Many ODE models

We derive a second-order ordinary differential equation (ODE), which is the limitof Nesterov’s accelerated gradient method. This ODE exhibits approximate equiv-alence to Nesterov’s scheme and thus can serve as a tool for analysis. We show thatthe continuous time ODE allows for a better understanding of Nesterov’s scheme.As a byproduct, we obtain a family of schemes with similar ...