A numerical technique for Volterra functional integral equations (VFIEs) with non-vanishing delays and fractional Bagley-Torvik equation is displayed in this work. The depends on Bernstein polynomial approximation. Numerical examples are utilized to evaluate the accurate results. findings figs tables show that simple use.

Fractional calculus is a natural extension of the integer order calculus and recently, a large number of applied problems have been formulated on fractional di¤erential equations. Analytical solution of many applications, where the fractional di¤erential equations appear, cannot be established. Therefore, cubic polynomial spline function is considered to …nd approximate solution for fractional ...

Inspired by the paper of Fazli and Nieto in [Open Math. 17 (2019) 499–512], we establish new existence uniqueness result for a type fractional Bagley–Torvik differential equation. Reported not only generalizes previous results but also adopts different technique. We finish this study concluding remarks which discuss preference our theorem compared to results. An example is constructed with spec...

This work proposes a valuable and successful strategy for approximating the solutions to Bagley–Torvik system, which plays an essential role in fractional calculus. The Caputo sense is used derive basic conformable fractional. problem numerically solved this study using effective symmetric projection method. From symmetry, there are some interesting original results. proposed approach has two k...

In this paper, Bernoulli wavelets are presented for solving (approximately) fractional differential equations in a large interval. Bernoulli wavelets operational matrix of fractional order integration is derived and utilized to reduce the fractional differential equations to system of algebraic equations. Numerical examples are carried out for various types of problems, including fractional Van...

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fraction...

Regular and singular perturbations of fractional ordinary differential equations (fODEs) are considered. This is likely the first attempt to describe these problems. Similarities and differences between these cases and the analogous ones for classical (integer-order) differential equations are pointed out. Examples, including the celebrated Bagley-Torvik equations are discussed. Asymptotic-nume...