Fractional powers of non-negative operators in Fréchet spaces.
Fractional -difference equations on the half line
This article deals with some results about the existence of solutions and bounded solutions and the attractivity for a class of fractional -difference equations. Some applications are made of Schauder fixed point theorem in Banach spaces and Darbo fixed point theorem in Fréchet spaces. We use some technics associated with the concept of measure of noncompactness and the diagonalization process. Some illustrative examples are given in the last section.
Fractional quantum integral inequalities.
Fractional regularization term for variational image registration.
Fractional Roesser problem and its optimization
In the paper, a fractional continuous Roesser model is considered. Existence and uniqueness of a solution and continuous dependence of solutions on controls of the nonlinear model are investigated. Next, a theorem on the existence of an optimal solution for linear model with variable coefficients is proved.
Fractional type operators in weighted generalized Hölder spaces.
Fractional virus epidemic model on financial networks
In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain...
Fractional-order variational calculus with generalized boundary conditions.
From Differences to Derivatives
A relation showing that the Grünwald-Letnikov and generalized Cauchy derivatives are equal is deduced confirming the validity of a well known conjecture. Integral representations for both direct and reverse fractional differences are presented. From these the fractional derivative is readily obtained generalizing the Cauchy integral formula.
From Newton's equation to fractional diffusion and wave equations.
Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition
The central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective...
General exact solvability conditions for the initial value problems for linear fractional functional differential equations
Conditions on the unique solvability of linear fractional functional differential equations are established. A pantograph-type model from electrodynamics is studied.
Generalized Boundary Value Problems for Nonlinear Fractional Langevin Equations
In this paper, generalized boundary value problems for nonlinear fractional Langevin equations is studied. Some new existence results of solutions in the balls with different radius are obtained when the nonlinear term satisfies nonlinear Lipschitz and linear growth conditions. Finally, two examples are given to illustrate the results.
Generalized Fractional Calculus With Application in Mechanics
Generalized Fractional Evolution Equation
2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20In this paper we study the generalized Riemann-Liouville (resp. Caputo) time fractional evolution equation in infinite dimensions. We show that the explicit solution is given as the convolution between the initial condition and a generalized function related to the Mittag-Leffler function. The fundamental solution corresponding to the Riemann-Liouville time fractional evolution equation does not admit a probabilistic...
Generalized fractional integrals on central Morrey spaces and generalized λ-CMO spaces
We introduce the generalized fractional integrals and prove the strong and weak boundedness of on the central Morrey spaces . In order to show the boundedness, the generalized λ-central mean oscillation spaces and the generalized weak λ-central mean oscillation spaces play an important role.
Generalized function fractional integration operators in some classes of analytic functions
Hamilton’s Principle with Variable Order Fractional Derivatives
MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf GorenfloWe propose a generalization of Hamilton’s principle in which the minimization is performed with respect to the admissible functions and the order of the derivation. The Euler–Lagrange equations for such minimization are derived. They generalize the classical Euler-Lagrange equation. Also, a new variational problem is formulated in the case when the order of the derivative is defined through a constitutive equation....
Hardy-type inequalities for integral transforms associated with Jacobi operator.
Heat kernel estimates for critical fractional diffusion operators
We construct the heat kernel of the 1/2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.