On a terminal value problem for parabolic reaction–diffusion systems with nonlocal coupled diffusivity terms

Hybrid Fibonacci wavelet method to solve fractional‐order logistic growth model

“…To solve the algebraic equation ( 35) using Newton iteration method, to find the Fibonacci coefficient g m,n (𝜁 ). To find the approximate solution, we put the values of g m,n (𝜁 ) in (34). Furthermore, 𝜇 2 (𝜁 ) is gained in the subsequent iteration.…”

“…To avoid confusion, the fractional derivative will be used throughout the rest of this article in the sense of Caputo. For further studies, we refer previous studies [31][32][33][34][35][36][37][38][39][40].…”

“…For any $$$ \zeta \in {\mathrm{\mathbb{R}}}^{+} $$$, the recurrence relation defines the Fibonacci polynomials as follows: $$$$ {\tilde{P}}_{n+2}\left(\zeta \right)=\zeta {\tilde{P}}_{n+1}\left(\zeta \right)+{\tilde{P}}_n\left(\zeta \right)\kern0.30em \left(n\in \mathrm{\mathbb{N}}\right), $$$$ with ICs $$$ {\tilde{P}}_0\left(\zeta \right)=0,{\tilde{P}}_1\left(\zeta \right)=1 $$$ [34].…”

On recovering the source term for the heat equation with memory term

“…-If m = 0 the problem (1.1) is called classical parabolic equation. This problem has been studied a lot in [9,11,10,2,18,20,12,22,21,5,17,19,14,13].…”