Related papers: Linear and nonlinear fractional Voigt models
We construct the existence theory for generalized fractional Bessel differential equations and find the solutions in the form of fractional or logarithmic fractional power series. We figure out the cases when the series solution is unique,…
A solution to the more than 300-years old problem of geometric and physical interpretation of fractional integration and differentiation (i.e., integration and differentiation of an arbitrary real order) is suggested for the…
Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
Fractional boundary value problems are often used to model complex systems and processes characterized by memory effects and anomalous diffusion. In this paper, we consider fractional boundary value problems involving the Riesz-Caputo…
In this paper, based on Newton interpolation we have proposed a numerical scheme of predictor-corrector type in order to solve fractional differential equations with the fractional derivative involving the Mittag-Leffler function. We have…
This paper investigates two classes of quasilinear and essentially nonlinear integral equations with a sum-difference kernel on the half-line. Such equations arise in various areas of physics, including the theory of radiative transfer in…
In this paper, we consider Caputo type fractional stochastic time-delay system with permutable matrices. We derive stochastic analogue of variation of constants formula via a newly defined delayed Mittag-Leffer type matrix function. Thus,…
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…
This paper investigates a nonlocal boundary value problem for a multi-parametric integral-differential equation involving the Caputo-Prabhakar type operator in a bounded rectangular domain. The nonlocal conditions are given as partial…
The subject of this paper is to derive the solution of generalized fractional kinetic equations. The results are obtained in a compact form containing the Mittag-Leffler function, which naturally occurs whenever one is dealing with…
We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined Caputo fractional derivative of variable order, are proved.…
We consider a fractional plasticity model based on linear isotropic and kinematic hardening as well as a standard von-Mises yield function, where the flow rule is replaced by a Riesz--Caputo fractional derivative. The resulting mathematical…
We discuss the existence of multiple positive solutions for a nonlocal fractional problem recently considered by Nieto and Pimental. Our approach relies on classical fixed point index.
We present some distinct asymptotic properties of solutions to Caputo fractional differential equations (FDEs). First, we show that the non-trivial solutions to a FDE can not converge to the fixed points faster than $t^{-\alpha}$, where…
This paper studies existence and uniqueness of solutions to generalized Volterra integral equations. Since our proof for existence and uniqueness does not make use of Banach fixed point theorem unlike the previous papers focused on this…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
In this work, we investigate a unique solvability of a direct and inverse source problem for a time-fractional partial differential equation with the Caputo and Bessel operators. Using spectral expansion method, we give explicit forms of…
Problems of calculus of variations with variable endpoints cannot be solved without transversality conditions. Here, we establish such type of conditions for fractional variational problems with the Caputo derivative. We consider: the…
This manuscript investigates the existence and uniqueness of solutions to the first order fractional anti-periodic boundary value problem involving Caputo-Katugampola (CK) derivative. A variety of tools for analysis this paper through the…