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Fifth-kind orthonormal Chebyshev polynomial solutions for fractional differential equations
The principal aim of the current paper is to present and analyze two new spectral algorithms
for solving some types of linear and nonlinear fractional-order differential equations. The …
for solving some types of linear and nonlinear fractional-order differential equations. The …
Mathematical modeling and analysis of two-variable system with noninteger-order derivative
The aim of this paper is to apply the newly trending Atangana-Baluanu derivative operator to
model some symbiosis systems describing commmensalism and predator-prey processes …
model some symbiosis systems describing commmensalism and predator-prey processes …
Shifted fifth-kind Chebyshev Galerkin treatment for linear hyperbolic first-order partial differential equations
Through the current article, a numerical technique to obtain an approximate solution of one-
dimensional linear hyperbolic partial differential equations is implemented. A certain …
dimensional linear hyperbolic partial differential equations is implemented. A certain …
A Tau approach for solving time-fractional heat equation based on the shifted sixth-kind Chebyshev polynomials
The time-fractional heat equation governed by nonlocal conditions is solved using a novel
method developed in this study, which is based on the spectral tau method. There are two …
method developed in this study, which is based on the spectral tau method. There are two …
Exploring ocean pH dynamics via a mathematical modeling with the Caputo fractional derivative
Global warming is a complex problem with far-reaching global implications. One of its
notable repercussions is the escalation of CO 2 levels in the atmosphere, resulting in the …
notable repercussions is the escalation of CO 2 levels in the atmosphere, resulting in the …
Advanced shifted sixth-kind Chebyshev tau approach for solving linear one-dimensional hyperbolic telegraph type problem
A new numerical scheme based on the tau spectral method for solving the linear hyperbolic
telegraph type equation is presented and implemented. The derivation of this scheme is …
telegraph type equation is presented and implemented. The derivation of this scheme is …
Spectral Galerkin schemes for a class of multi-order fractional pantograph equations
In this paper, we study and present a spectral numerical technique for solving a general
class of multi-order fractional pantograph equations with varying coefficients and systems of …
class of multi-order fractional pantograph equations with varying coefficients and systems of …
Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model
This study is to introduce a novel design and implementation of a neuro-swarming
computational numerical procedure for numerical treatment of the fractional Bagley–Torvik …
computational numerical procedure for numerical treatment of the fractional Bagley–Torvik …
Spectral tau algorithm for certain coupled system of fractional differential equations via generalized Fibonacci polynomial sequence
This paper concerns new numerical solutions for certain coupled system of fractional
differential equations through the employment of the so-called generalized Fibonacci …
differential equations through the employment of the so-called generalized Fibonacci …
Modified Galerkin algorithm for solving multitype fractional differential equations
The primary point of this manuscript is to dissect and execute a new modified Galerkin
algorithm based on the shifted Jacobi polynomials for solving fractional differential …
algorithm based on the shifted Jacobi polynomials for solving fractional differential …