English
Related papers

Related papers: Variational Problems Involving a Caputo-Type Fract…

200 papers

In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for…

Statistical Mechanics · Physics 2017-07-18 Xiao-Jun Yang , J. A. Tenreiro Machado

The calculus of variations for lagrangians which are not functions on the tangent bundle, but sections certain affine bundles is developed. We follow a general approach to variational principles which admits boundary terms of variations.

Mathematical Physics · Physics 2007-05-23 Katarzyna Grabowska , Pawel Urbanski

The aim of this study to investigate the existence of solutions for the following nonlocal integral boundary value problem of Caputo type fractional differential inclusions. To achieve our goals, we take advantage of fixed point theorems…

Classical Analysis and ODEs · Mathematics 2018-07-17 Hüseyin Işık

We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these…

Functional Analysis · Mathematics 2015-05-27 Teodor M. Atanackovic , Sanja Konjik , Stevan Pilipovic

We study epidemic Susceptible-Infected-Susceptible models in the fractional setting. The novelty is to consider models in which the susceptible and infected populations evolve according to different fractional orders. We study a model based…

Optimization and Control · Mathematics 2021-07-08 Caterina Balzotti , Mirko D'Ovidio , Anna Chiara Lai , Paola Loreti

In this paper, the fractional differential matrices based on the Jacobi-Gauss points are derived with respect to the Caputo and Riemann-Liouville fractional derivative operators. The spectral radii of the fractional differential matrices…

Numerical Analysis · Mathematics 2015-11-05 Fanhai Zeng , Changpin Li

In this paper, we deal with a Cauchy problem for a nonlinear fractional differential equation with the Caputo derivative of order $\alpha \in (0, 1)$. As initial data, we consider a pair consisting of an initial point, which does not…

Optimization and Control · Mathematics 2022-08-23 Mikhail I. Gomoyunov

The present paper is devoted to constructing L2 type difference analog of the Caputo fractional derivative. The fundamental features of this difference operator are studied and it is used to construct difference schemes generating…

Numerical Analysis · Mathematics 2021-02-18 Anatoly A. Alikhanov , Chengming Huang

This paper deals with the fractional Caputo--Fabrizio derivative and some basic properties related. A computation of this fractional derivative to power functions is given in terms of Mittag--Lefler functions. The inverse operator named the…

Analysis of PDEs · Mathematics 2018-09-10 Sabrina Roscani , Domingo Tarzia , Lucas Venturato

In this PhD thesis, we deal with problems related to nonlocal operators, in particular to the fractional Laplacian and to some other types of fractional derivatives (the Caputo and the Marchaud derivatives). We make an extensive…

Analysis of PDEs · Mathematics 2017-05-03 Claudia Bucur

We set the main concepts for multiplicative fractional calculus. We define Caputo, Riemann and Letnikov multiplicative fractional derivatives and multiplicative fractional integrals and study some of their properties. Finally, the…

Classical Analysis and ODEs · Mathematics 2016-09-20 Thabet Abdeljawad

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 consider the time-fractional Cattaneo equation involving the tempered Caputo space-fractional derivative. We find the characteristic function of the related process and we explain the main differences with previous stochastic treatments…

Probability · Mathematics 2022-06-13 Luisa Beghin , Roberto Garra , Francesco Mainardi , Gianni Pagnini

The L-fractional derivative is defined as a certain normalization of the well-known Caputo derivative, so alternative properties hold: smoothness and finite slope at the origin for the solution, velocity units for the vector field, and a…

Classical Analysis and ODEs · Mathematics 2024-07-16 Marc Jornet

In this paper, we first provide a short summary of the main properties of the so-called general fractional derivatives with the Sonin kernels introduced so far. These are integro-differential operators defined as compositions of the first…

Classical Analysis and ODEs · Mathematics 2022-08-03 Yuri Luchko

In this paper we prove that local fractional derivatives of differentiable functions are integer-order derivative or zero operator. We demonstrate that the local fractional derivatives are limits of the left-sided Caputo fractional…

Classical Analysis and ODEs · Mathematics 2018-01-26 Vasily E. Tarasov

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…

Optimization and Control · Mathematics 2016-12-26 O. S. Fard , R. Almeida , J. Soolaki , A. H. Borzabadi

An adaptive finite difference scheme for variable-order fractional-time subdiffusion equations in the Caputo form is studied. The fractional time derivative is discretized by the L1 procedure but using nonhomogeneous timesteps. The size of…

Numerical Analysis · Mathematics 2024-09-20 Joaquín Quintana-Murillo , Santos Bravo Yuste

This paper systematically treats the asymptotic behavior of many (linear/nonlinear) classes of higher-order fractional differential equations with multiple terms. To do this, we utilize the characteristics of Caputo fractional…

Dynamical Systems · Mathematics 2024-10-15 H. D. Thai , H. T. Tuan

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…

General Mathematics · Mathematics 2019-11-21 Saleh S. Redhwan , Sadikali L. Shaikh , Mohammed S. Abdo