In this research article, we develop a powerful algorithm for numerical solutions to variable-
order partial differential equations (PDEs). For the said method, we utilize properties of …

The fractional reaction–subdiffusion problem is one of the most well-known subdiffusion
models extensively used for simulating numerous physical processes in recent years. This …

This paper is concerned with a highly accurate numerical scheme for a class of one-and two-
dimensional time-fractional advection-reaction-subdiffusion equations of variable-order α (x …

The focus of this work is to construct a pseudo-operational Jacobi collocation scheme for
numerically solving the Caputo variable-order time-fractional diffusion-type equations with …

In this paper, the Vieta–Fibonacci wavelets as a new family of orthonormal wavelets are
generated. An operational matrix concerning fractional integration of these wavelets is …

In this paper, the variable order fractional derivative in the Heydari-Hosseininia sense is
employed to define a new fractional version of 2D reaction-advection-diffusion equation. An …

In this paper, we introduce a numerical technique for solving the Cauchy non-homogeneous
time-fractional diffusion-wave equation with the Caputo derivative operator. The key idea …

In this paper, we design a new computational algorithm for solving fractal–fractional optimal
control and variational problems. To attain the proposed goal, we exert Pell–Lucas …

Abstract Fractional Fokker–Planck equation plays an important role in describing anomalous
dynamics. In this paper, we consider a spectral method for the spatio-temporal coupled …

In this paper, we propose a hybrid numerical method based on the weighted finite difference
and the quintic Hermite collocation methods. The proposed method is used for solving the …