This article introduces two numerical methods to address boundary value problems
associated with secondorder and fractional differential equations. These methods employ …

This paper presents a new algorithm for resolving linear and non-linear second-order Robin
boundary value problems (BVPS) and the Bratu-type equations in one and two dimensions …

This paper presents a new method to numerically solve the nonlinear time-fractional
generalized Kawahara equations (NTFGKE) with uniform initial boundary conditions (IBCs) …

This study presents a new efficient collocation approach to handle the nonlinear generalized
fractional Riccati equation. The linearization formula of the product of two shifted Chebyshev …

In the present paper, we construct a set of multiscale orthonormal basis based on Legendre
polynomials. Using this orthonormal basis, a new algorithm is designed for solving the …

In this paper, we demonstrate the local well-posedness and blow up of solutions for a class
of time-and space-fractional diffusion wave equation in a fractional power space associated …

In this study, we utilize a specific combination of orthogonal Gegenbauer polynomials as
basis functions that satisfy homogeneous boundary conditions in the spatial variable and …

The ionosphere near the equatorial ionization anomaly crest region in the Indian
ionospheric sector was studied from May 2016 to April 2017, a solar minimum period. Total …

This research focuses on the development of a streamlined numerical technique founded on
the hybridization of two shifted polynomial basis functions to address a specific category of …

The study investigates thermal interactions in a two-dimensional time fractional-order
thermoelastic problem in a homogeneous, isotropic, and perfectly conducting thick annular …