Based on [4], we produce a collection of interesting trigonometric and hyperbolic Taylor
formulae with integral remainders. Using these we derive Opial and Ostrowski type …

In this study, we construct new numerical methods for solving the initial value problem (IVP)
in ordinary differential equations based on a symmetrical quadrature integration formula …

This study is devoted to studying the existence and uniqueness of solutions for Hadamard
implicit fractional differential equations with generalized Hadamard fractional integro …

In this work a hybrid scheme is proposed for the numerical study of various evolutionary
partial differential equations (EPDEs). In proposed strategy, temporal derivatives are …

This research aims to propose a new family of one-parameter multi-step iterative methods
that combine the homotopy perturbation method with a quadrature formula for solving …

The aim of this paper is to establish various factorization results and then to derive estimates
for linear functionals through the use of a generalized Taylor theorem. Additionally, several …

The goal of this paper is to consider a differential equation system written as an interesting
equivalent form that has not been used before. Using Perov's fixed point theorem in …

This paper introduces a new modification to an iterative method for solving Cauchy
problems (IVPs) based on an inverse polynomial technique. The proposed method is proven …

In this paper, we study the approximation of unbounded functions in a weighted space by
modulus of smoothness using various linear operators. We establish direct theorems for …

In this paper, we propose a new numerical scheme based on a variation of the standard
formulation of the Runge–Kutta method using Taylor series expansion for solving initial …