In this study, we present an innovative approach involving a spectral collocation algorithm to
effectively obtain numerical solutions of the nonlinear time-fractional generalized Kawahara …

The time-fractional diffusion equation is applied to a wide range of practical applications. We
suggest using a potent spectral approach to solve this equation. These techniques' main …

In this article, we present two numerical methods for treating the fractional initial‐value
problem (FIVP) and time‐fractional partial differential problem (FPDP) that caused the error …

Herein, we build and implement a combination of Lucas polynomials basis that fulfills the
spatial homogenous boundary conditions. This basis is then used to solve the time-fractional …

In this work, first, a family of fourth‐order methods is proposed to solve nonlinear equations.
The methods satisfy the Kung‐Traub optimality conjecture. By developing the methods into …

This article proposes a numerical algorithm utilizing the spectral Tau method for numerically
handling the Kawahara partial differential equation. The double basis of the fifth-kind …

The goal of this study is to suggest a new general triple integral transform known as Gamar
transform. Next, we compare the current transform to a number of existing triple integral …

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 …

Because of its flexibility and multiple meanings, the concept of information entropy in its
continuous or discrete form has proven to be very relevant in numerous scientific branches …

This paper explores the application of fuzzy theory to solve fractional heat equations using a
novel approach, the Optimal Homotopy Asymptotic Method (OHAM). We introduce a semi …