A new representation for the solution of the Richards‐type fractional differential equation.

Richards in [35] proposed a modification of the logistic model to model growth of biological populations. In this paper, we give a new representation (or characterization) of the solution to the Richards‐type fractional differential equation Dαy(t)=y(t)·(1+a(t)yβ(t))$$ {\mathcal{D}}^{\alpha }y(t)=y(t)\cdotp \left(1+a(t){y}^{\beta }(t)\right) $$ for t≥0$$ t\ge 0 $$, where a:[0,∞)→ℝ$$ a:\left[0,\infty \right)\to \mathrm{\mathbb{R}} $$ is a continuously differentiable function on [0,∞),α∈(0,1)$$ \left[0,\infty \right),\alpha \in \left(0,1\right) $$ and β$$ \beta $$ is a positive real constant. The obtained representation of the solution can be used effectively for computational and analytic purposes. This study improves and generalizes the results obtained on fractional logistic ordinary differential equation. [ABSTRACT FROM AUTHOR]