English
Related papers

Related papers: Analysis of some generalized ABC- fractional logis…

200 papers

In this article, a new reproducing kernel approach is developed for obtaining numerical solution of nonlinear three-point boundary value problems with fractional order. This approach is based on reproducing kernel which is constructed by…

Numerical Analysis · Mathematics 2020-01-20 Mehmet Giyas Sakar , Onur Saldır

In this article, we show that multilinear fractional type operators are bounded from product Hardy spaces with variable exponents into Lebesgue spaces with variable exponents via the atomic decomposition theory. We also study continuity…

Classical Analysis and ODEs · Mathematics 2019-07-19 Jian Tan

The aim of this paper is to present a linear viscoelastic model based on Prabhakar fractional operators. In particular, we propose a modification of the classical fractional Maxwell model, in which we replace the Caputo derivative with the…

Mathematical Physics · Physics 2017-08-10 Andrea Giusti , Ivano Colombaro

In this paper the singular Emden-Fowler equation of fractional order is introduced and a computational method is proposed for its numerical solution. For the approximation of the solutions we have used Boubaker polynomials and defined the…

Numerical Analysis · Mathematics 2022-02-28 Abdelkrim Bencheikh , Lakhdar Chiter

In this paper, we develop the theory of nonlinear hybrid fractional differential equations involving Atangana--Baleanu--Caputo (ABC) fractional derivative. We construct the equivalent fractional integral equation and establish the existence…

Dynamical Systems · Mathematics 2021-02-03 Sagar T. Sutar , Kishor D. Kucche

In the paper, a linear differential equation with variable coefficients and a Caputo fractional derivative is considered. For this equation, a Cauchy problem is studied, when an initial condition is given at an intermediate point that does…

Optimization and Control · Mathematics 2020-09-01 Mikhail Gomoyunov

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.

Optimization and Control · Mathematics 2013-02-07 Tatiana Odzijewicz , Agnieszka B. Malinowska , Delfim F. M. Torres

In this work, we consider boundary value problems involving Caputo and Riemann-Liouville fractional derivatives of order $\alpha\in(1,2)$ on the unit interval $(0,1)$. These fractional derivatives lead to non-symmetric boundary value…

Numerical Analysis · Mathematics 2013-07-19 Bangti Jin , Raytcho Lazarov , Joseph Pasciak

In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…

Analysis of PDEs · Mathematics 2014-03-06 Roberto Garra , Federico Polito

We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional…

Analysis of PDEs · Mathematics 2018-11-12 Moulay Rchid Sidi Ammi , Delfim F. M. Torres

The main goal of this work is to perform a nonolonomic deformation (Fedosov type) quantization of fractional Lagrange geometries. The constructions are provided for a (fractional) almost Kahler model encoding equivalently all data for…

Mathematical Physics · Physics 2011-01-05 Dumitru Baleanu , Sergiu I. Vacaru

The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the…

Mathematical Physics · Physics 2008-05-18 Francesco Mainardi , Rudolf Gorenflo

An initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For this problem, we give a simple framework…

Numerical Analysis · Mathematics 2018-10-24 Natalia Kopteva

Fractional difference sequence spaces have been studied in the literature recently. In this work, some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some difference…

Functional Analysis · Mathematics 2019-02-22 Faruk Özger

In this paper, we consider a class of the Caputo fractional stochastic differential equations of fractional order $\alpha \in (\frac{1}{2},1]$. Our aim is to analyze of the continuous dependence of solutions on the fractional order…

Probability · Mathematics 2025-06-04 T. C. Son , N. T. Dung , P. T. P Thuy , T. M. Cuong , H. T. P. Thao , P. D. Tung

This paper is concerned with the investigation of the controllability and observability of Caputo fractional differential linear systems of any real order {\alpha} . Expressions for the expansions of the evolution operators in powers of the…

Dynamical Systems · Mathematics 2010-10-04 M. De La Sen

The main theme of this paper is to give sufficient conditions for the weighted boundedness of the bilinear fractional integral operator $\mathsf{BI}_\al$. The proposed condition involves the union of multilinear Muckenhoupt-type conditions.…

Functional Analysis · Mathematics 2025-07-22 Cong Hoang

In this article, we deal with fractional stochastic differential equations, so-called Caputo type fractional backward stochastic differential equations (Caputo fBSDEs, for short), and study the well-posedness of an adapted solution to…

Probability · Mathematics 2022-10-05 Nazim I. Mahmudov , Arzu Ahmadova

The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…

Numerical Analysis · Mathematics 2020-08-26 Alberto Ferrari , Manuel Gadella , Luis Lara , Eduardo Santillan Marcus

We present a general series representation formula for the local solution of Bernoulli equation with Caputo fractional derivatives. We then focus on a generalization of the fractional logistic equation and we present some related numerical…

Optimization and Control · Mathematics 2021-05-06 Mirko D'Ovidio , Anna Chiara Lai , Paola Loreti