In this paper, we study diffusion equations involving Hadamard-type time-fractional derivatives related to ultra-slow random models. We start our analysis using the abstract fractional Cauchy problem, replacing classical time derivative with Hadamard operator. The stochastic meaning of introduced differential equation is provided, and application particular case heat then discussed in detail. b...

Fractional integro-differential equations arise in the mathematical modelling of various physical phenomena like heat conduction in materials with memory, diffusion processes etc. In this paper, we have taken the fractional integro-differential equation of type Dy(t) = a(t)y(t) + f(t) + ∫ t

A corrected derivation of nonlinear wave propagation equations with fractional loss operators is presented. The fundamental approach is based on fractional formulations of the stress-strain and heat flux definitions but uses the energy equation and thermodynamic identities to link density and pressure instead of an erroneous fractional form of the entropy equation as done in Prieur and Holm ["N...

In this effort, we propose a new fractional differential operator in the open unit disk. The is an extension of Atangana-Baleanu without singular kernel. We suggest it for normalized class analytic functions By employing extended operator, study time-2-D space heat equation and optimizing its solution by chaotic function.

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...

We describe the large-time asymptotics of solutions to heat equation for fractional Laplacian with added subcritical or even critical Hardy-type potential. The is governed by a self-similar solution equation, obtained as normalized limit at origin kernel corresponding Feynman-Kac semigroup.

In this paper, a new theory of generalized micropolar thermoelasticity is derived by using fractional calculus. The generalized heat conduction equation in micropolar thermoelasticity has been modified with two distinct temperatures, conductive temperature and thermodynamic temperature by fractional calculus which depends upon the idea of the RiemannLiouville fractional integral operators. A un...