Results 1 to 10 of about 244 (107)

Degenerate Multi-Term Equations with Gerasimov–Caputo Derivatives in the Sectorial Case [PDF]

Mathematics, 2022
The unique solvability for the Cauchy problem in a class of degenerate multi-term linear equations with Gerasimov–Caputo derivatives in a Banach space is investigated.
Vladimir E. Fedorov, Kseniya V. Boyko
doaj   +5 more sources

Inverse Problem for Evolutionary Equation with the Gerasimov – Caputo Fractional Derivative in the Sectorial Case

Известия Иркутского государственного университета: Серия "Математика", 2019
We investigates the unique solvability of a class of linear inverse problems with a time-independent unknown coefficient in an evolution equation in Banach space, which is resolved with respect to the fractional Gerasimov – Caputo derivative.
V.E. Fedorov, A. V. Nagumanova
doaj   +4 more sources

Generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator [PDF]

Қарағанды университетінің хабаршысы. Математика сериясы, 2022
This paper formulates and solves a generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator.
L.Kh. Gadzova
doaj   +6 more sources

A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order. [PDF]

Comput Math Methods Med, 2022
The purpose of this paper is to investigate the approximate solution of the casting‐mould heterogeneous system with Caputo derivative under the homotopy idea. The symmetry design of the system contains the integer partial differential equations and the fractional‐order partial differential equations. We apply Yang transform homotopy perturbation method
Luo X, Nadeem M, Asjad MI, Abdo MS.
europepmc   +2 more sources

Integrated Resolving Functions for Equations with Gerasimov–Caputo Derivatives

Symmetry, 2023
The concept of a β-integrated resolving function for a linear equation with a Gerasimov–Caputo fractional derivative is introduced into consideration. A number of properties of such functions are proved, and conditions for the solvability of the Cauchy problem to linear homogeneous and inhomogeneous equations are found in the case of the existence of a
Vladimir Fedorov, Anton Skorynin, Amar Debbouche   +2 more
exaly   +2 more sources

A fractional equation with left-sided fractional Bessel derivatives of Gerasimov-Caputo type [PDF]

, 2019
In this article we propose and study a method to solve ordinary differential equations with left-sided fractional Bessel derivatives on semi-axes of Gerasimov-Caputo type.
Shishkina, E., Sitnik, S.
core   +3 more sources

The optimization problem for determining the functional dependence of the variable order of the fractional derivative of the Gerasimov-Caputo type

Вестник КРАУНЦ. Физико-математические науки
При решении задач математического моделирования часто приходится обращаться к теории интегрально-дифференциального исчисления. С ее помощью можно описывать динамические процессы самой разной природы. Использование аппарата дробных производных позволяет уточнить некоторые из этих моделей за счет учета в уравнениях эффекта памяти.
Tvërdyĭ, Dmitriĭ Aleksandrovich, Parovik, Roman Ivanovich   +1 more
exaly   +2 more sources

Application of the Riccati hereditary mathematical model to the study of the dynamics of radon accumulation in the storage chamber [PDF]

EPJ Web of Conferences, 2021
The article proposes a mathematical model of radon accumulation in a chamber, which takes into account the hereditary properties of the environment in which radon migrates.
Tverdyi Dmitryi, Parovik Roman, Makarov Evgeniy, Firstov Pavel, Alimova Nazira   +4 more
doaj   +1 more source

Sturm-Liouville Problem with Mixed Boundary Conditions for a Differential Equation with a Fractional Derivative and Its Application in Viscoelasticity Models

Axioms, 2023
In this study, we obtained a system of eigenfunctions and eigenvalues for the mixed homogeneous Sturm-Liouville problem of a second-order differential equation containing a fractional derivative operator.
Ludmila Kiryanova, Tatiana Matseevich
doaj   +1 more source

Investigation of Finite-Difference Schemes for the Numerical Solution of a Fractional Nonlinear Equation

Fractal and Fractional, 2021
The article discusses different schemes for the numerical solution of the fractional Riccati equation with variable coefficients and variable memory, where the fractional derivative is understood in the sense of Gerasimov-Caputo.
Dmitriy Tverdyi, Roman Parovik
doaj   +1 more source