This manuscript aims to study a modified predator–prey model's existence, stability, and
dynamics under the newly developed fractal–fractional order operator in the Caputo …

Fluids like hybrid nanofluids have great potential that present exceptional thermal behavior
and thermophysical properties as compare to ordinary nanofluids. Hybrid nanofluids are …

This study manages the numeric roots of the 7th-order linear & nonlinear boundary value
problems (BVPs) utilizing another CB (Cubic-B) spline strategy. Cubic Spline interpolation is …

This paper is devoted to developing spectral solutions for the nonlinear fractional Klein–
Gordon equation. The typical collocation method and the tau method are employed for …

In this study we propose a fractional frequency flexible Fourier form fractionally integrated
ADF unit-root test, which combines the fractional integration and nonlinear trend as a form of …

The algebras of the symmetry operators for the Klein–Gordon equation are important for a
charged test particle, moving in an external electromagnetic field in a space time manifold …

In this work, we solve a new kind of the fractional Klein–Gordon problem numerically. In fact,
we study the mentioned problem under fractal–fractional operator with the Riemann …

In this paper, the dynamical behavior of a mathematical model of cancer including tumor
cells, immune cells, and normal cells is investigated when a delay term is induced. Though …

This paper addresses a new spectral collocation method for solving nonlinear fractional
quadratic integral equations. The main idea of this method is to construct the approximate …

Investigation of spectral (collocation or Galerkin) methods for the solution approximation of
different classes of optimal control problems have had been increased in recent years. In …