Bifractional reaction-diffusion equation with logarithmic memory kernel.

In this work, we study a bifractional reaction-diffusion equation with generalized temporal memory and nonlocal spatial diffusion. The temporal dynamics are modeled using the Hilfer-type fractional derivative with respect to a logarithmic scale function ψ (t) = ln(1+t), following the generalized approach of Vanterler et al. [3]. The spatial operator is the Riesz-Feller derivative, capturing nonlocality and asymmetry [6, 16]. Analytical solutions for the linear reaction case are obtained via the Fourier transform in space and the generalized ψ -Laplace transform in time, expressed in terms of Mittag-Leffler functions and propose the numerical calculation for this solutions.