Boundary value problem for a multidinensional system of equations with Riemann–Liouvile fractional derivatives

Мамчуев, М. О.

doi:10.33048/semi.2019.16.049

Cited by 4 publications

(3 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that [13,14] investigated boundary value problems for multidimensional systems of partial differential equations of fractional order. In [15] attention was drawn to the fact that in the one-dimensional case these results coincide with the results of [4].…”

Section: Introductionmentioning

confidence: 99%

Cauchy Problem for a Linear System of Ordinary Differential Equations of the Fractional Order

Мамчуев

2020

Mathematics

View full text Add to dashboard Cite

We investigate the initial problem for a linear system of ordinary differential equations with constant coefficients and with the Dzhrbashyan–Nersesyan fractional differentiation operator. The existence and uniqueness theorems of the solution of the boundary value problem under the study are proved. The solution is constructed explicitly in terms of the Mittag–Leffler function of the matrix argument. The Dzhrbashyan–Nersesyan operator is a generalization of the Riemann–Liouville, Caputo and Miller–Ross fractional differentiation operators. The obtained results as particular cases contain the results related to the study of initial problems for the systems of ordinary differential equations with Riemann–Liouville, Caputo and Miller–Ross derivatives and the investigated initial problem that generalizes them.

show abstract

Section: Introductionmentioning

confidence: 99%

Cauchy Problem for a Linear System of Ordinary Differential Equations of the Fractional Order

Мамчуев

2020

Mathematics

View full text Add to dashboard Cite

show abstract

“…Note that [13] and [14] investigated boundary value problems for multidimensional systems of partial differential equations of fractional order. In [15], attention was drawn to the fact that in the one-dimensional case these results coincide with the results of [4].…”

Section: Introductionmentioning

confidence: 99%

Cauchy Problem for a Linear System of Ordinary Differential Equations of the Fractional Order

Мамчуев¹

2020

Preprint

View full text Add to dashboard Cite

The paper investigates the initial problem for a linear system of ordinary differential equations with the fractional differentiation operator Dzhrbashyan -Nersesyan with constant coefficients. The existence and uniqueness theorems of the solution of the boundary value problem under study are proved. The solution is constructed explicitly in terms of the Mittag-Leffler function of the matrix argument. The Dzhrbashyan -Nersesyan operator is a generalization of the Riemann -Liouville, Caputo and Miller-Ross fractional differentiation operators. The obtained results as special cases contain results related to the study of initial problems for systems of ordinary differential equations with Riemann -Liouville, Caputo and Miller -Ross derivativess, and the investigated initial problem generalizes them.

show abstract

“…Regular case of the invertible operator L was studied in [4,29]. Mamchuev [34] studied the boundary value problem for the fractional order system of the form…”

mentioning

confidence: 99%

On a Method of Solution of Systems of Fractional Pseudo-Differential Equations

Umarov

Ashurov

Chen

2021

Fract Calc Appl Anal

View full text Add to dashboard Cite

This paper is devoted to the general theory of linear systems of fractional order pseudo-differential equations. Single fractional order differential and pseudo-differential equations are studied by many authors and several monographs and handbooks have been published devoted to its theory and applications. However, the state of systems of fractional order ordinary and partial or pseudo-differential equations is still far from completeness, even in the linear case. In this paper we develop a new method of solution of general systems of fractional order linear pseudo-differential equations and prove existence and uniqueness theorems in the special classes of distributions, as well as in the Sobolev spaces.

show abstract

Boundary value problem for a multidinensional system of equations with Riemann–Liouvile fractional derivatives

Cited by 4 publications

References 5 publications

Cauchy Problem for a Linear System of Ordinary Differential Equations of the Fractional Order

Cauchy Problem for a Linear System of Ordinary Differential Equations of the Fractional Order

Cauchy Problem for a Linear System of Ordinary Differential Equations of the Fractional Order

On a Method of Solution of Systems of Fractional Pseudo-Differential Equations

Contact Info

Product

Resources

About