Related papers: Time-fractional derivatives in relaxation processe…
The friction force is derived using fractional calculus by considering the non-uniform flow of time in dissipative processes. The approach incorporates inhomogeneous velocity without unphysical approximations, resulting in a Lagrangian…
This paper is concerned with the fractional evolution equation with a discrete distribution of Caputo time-derivatives such that the largest and the smallest orders, $\alpha$ and $\alpha_m$, satisfy the conditions $1<\alpha\le 2$ and…
The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved…
A general fractional relaxation equation is considered with a convolutional derivative in time introduced by A. Kochubei (Integr. Equ. Oper. Theory 71 (2011), 583-600). This equation generalizes the single-term, multi-term and…
In order to describe more complex problem using the concept of fractional derivatives, we introduce in this paper the concept of fractional derivatives with orders. The new definitions are based upon the concept of power law together with…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…
We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…
This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of enhanced diffusing movements of random turbulent particle resulting from nonlinear inertial interactions. A combined effect of the inertial…
A natural consequence of the fractional calculus is its extension to a matrix order of differentiation and integration. A matrix-order derivative definition and a matrix-order integration arise from the generalization of the gamma function…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
We establish partial semigroup property of Riemann-Liouville and Caputo fractional differential operators. Using this result we prove theorems on reduction of multi-term fractional differential systems to single-term and multi-order…
In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian…
The study of fuzzy fractional variational problems in terms of a fractional Liouville-Caputo derivative is introduced. Necessary optimality conditions for problems of the fuzzy fractional calculus of variations with free end-points are…
In this paper we identify, for small $t$ and a fixed $T>0,$ the order $\alpha>0$ in the abstract fractional differential equation $$\partial^\alpha u(t)=Au(t),$$ where the time-fractional derivative $\partial^\alpha$ is understood in the…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
We review some fractional free boundary problems that were recently considered for modeling anomalous phase-transitions. All problems are of Stefan type and involve fractional derivatives in time according to Caputo's definition. We survey…
The stochastic scenario of relaxation in the complex systems is presented. It is based on a general probabilistic formalism of limit theorems. The nonexponential relaxation is shown to result from the asymptotic self-similar properties in…
The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical…
The momentous objective of this work is to discuss some qualitative properties of solutions such as the estimate on the solutions, the continuous dependence of the solutions on initial conditions as well as the existence and uniqueness of…
We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous…