This paper presents a fractional mathematical model of a one-dimensional phase-change problem (Stefan problem) with a variable latent-heat (a power function of position). This model includes space–time fractional derivatives in the Caputo sense and time-dependent surface-heat flux. An approximate solution of this model is obtained by using the optimal homotopy asymptotic method to find the solu...

Zolotarev proved a duality result that relates stable densities with different indices. In this paper, we show how Zolotarev duality leads to some interesting results on fractional diffusion. Fractional diffusion equations employ fractional derivatives in place of the usual integer order derivatives. They govern scaling limits of random walk models, with power law jumps leading to fractional de...

The economic burden of HIV extends beyond the individual level and affects communities countries. can lead to decreased growth due lost productivity increased healthcare costs. In some countries, epidemic has led a reduction in life expectancy, which impact overall quality prosperity. Therefore, it is significant investigate intricate dynamics this viral infection know how virus interacts with ...

Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establ...

A fundamental aspect of harmonic analysis on Euclidean spaces deals with various classes of real or complex-valued functions, such as the C classes of functions which are continuous and continuously differentiable up to order k, where k is a nonnegative integer. If k = 0, this simply means that the function is continuous. Of course continuity of a function makes sense on any metric space, or on...

In the paper, we prove discrete universality theorem in sense of weak convergence probability measures space analytic functions for L-functions elliptic curves. We consider an approximation by translations LE (s+imh) , where h > 0 is a fixed number, imaginary part complex variable take values from some set such as arithmetical progression. suppose that number chosen so exp{2πk/h } rational n...

: Singular systems play an important role in many fields, and some new fractional operators, which are general, have been proposed recently. Therefore, singular on the basis of mixed derivatives including integer order derivative generalized operators studied. Firstly, Lagrange equations within established, primary constraints presented for systems. Then constrained Hamilton constructed by intr...

Gravitational lenses on galaxy scales are plausibly modelled as having ellipsoidal symmetry and a universal dark matter density profile, with a Sersic profile to describe the distribution of baryonic matter. Predicting all lensing effects requires knowledge of the total lens potential: in this work we give analytic forms for that of the above hybrid model. Emphasising that complex lens potentia...