On the cauchy problem for a class differential inclusions of fractional order with an almost lower semicontinuous right part

10.12737/6747 ◽  
2014 ◽  
Vol 2 (5) ◽  
pp. 49-51
Author(s):  
G. Petrosyan
Keyword(s):  
Cauchy Problem ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Lower Semicontinuous ◽  
The Cauchy Problem

Mkhitar Djrbashian and his contribution to Fractional Calculus

2020 ◽  
Vol 23 (6) ◽  
pp. 1797-1809
Author(s):  
Sergei Rogosin ◽  
Maryna Dubatovskaya
Keyword(s):  
Cauchy Problem ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Approximation Theory ◽  
Fractional Derivatives ◽  
Complex Analysis ◽  
Integral Transforms ◽  
Modern Theory ◽  
Survey Paper ◽  
The Cauchy Problem

Abstract This survey paper is devoted to the description of the results by M.M. Djrbashian related to the modern theory of Fractional Calculus. M.M. Djrbashian (1918-1994) is a well-known expert in complex analysis, harmonic analysis and approximation theory. Anyway, his contributions to fractional calculus, to boundary value problems for fractional order operators, to the investigation of properties of the Queen function of Fractional Calculus (the Mittag-Leffler function), to integral transforms’ theory has to be understood on a better level. Unfortunately, most of his works are not enough popular as in that time were published in Russian. The aim of this survey is to fill in the gap in the clear recognition of M.M. Djrbashian’s results in these areas. For same purpose, we decided also to translate in English one of his basic papers [21] of 1968 (joint with A.B. Nersesian, “Fractional derivatives and the Cauchy problem for differential equations of fractional order”), and were invited by the “FCAA” editors to publish its re-edited version in this same issue of the journal.

scholarly journals On the solution sets to differential inclusions on an unbounded interval

2000 ◽  
Vol 43 (3) ◽  
pp. 475-484 ◽  
Author(s):  
Vasile Staicu
Keyword(s):  
Cauchy Problem ◽  
Differential Inclusions ◽  
Solution Sets ◽  
Unbounded Interval ◽  
The Cauchy Problem ◽  
Image Position ◽  
Derivatives Of

AbstractWe prove that for F: [0,∞) × ℝn → K (ℝn) a Lipschitzian multifunction with compact values, the set of derivatives of solutions of the Cauchy problemis a retract of

scholarly journals THE MAXIMUM PRINCIPLE FOR THE EQUATION OF LOCAL FLUCTUATIONS OF RIESZ GRAVITATIONAL FIELDS OF PURELY FRACTIONAL ORDER

2021 ◽  
Vol 9 (2) ◽  
pp. 81-91
Author(s):  
V. Litovchenko
Keyword(s):  
Cauchy Problem ◽  
Maximum Principle ◽  
Fractional Order ◽  
Moving Objects ◽  
Riesz Potential ◽  
Pseudodifferential Equation ◽  
Time Interval ◽  
The Maximum Principle ◽  
Gravitational Fields ◽  
The Cauchy Problem

The parabolic pseudodifferential equation with the Riesz fractional differentiation operator of α ∈ (0; 1) order, which acts on a spatial variable, is considered in the paper. This equation naturally summarizes the known equation of fractal diffusion of purely fractional order. It arises in the mathematical modeling of local vortices of nonstationary Riesz gravitational fields caused by moving objects, the interaction between the masses of which is characterized by the corresponding Riesz potential. The fundamental solution of the Cauchy problem for this equati- on is the density distribution of the probabilities of the force of local interaction between these objects, it belongs to the class of Polya distributions of symmetric stable random processes. Under certain conditions, for the coefficient of local field fluctuations, an analogue of the maximum principle was established for this equation. This principle is important in particular for substantiating the unity of the solution of the Cauchy problem on a time interval where the fluctuation coefficient is a non-decreasing function.

scholarly journals A note on the Cauchy problem for differential inclusions

1993 ◽  
Vol 1 (2) ◽  
pp. 315 ◽  
Author(s):  
Marlène Frigon ◽  
Andrzej Granas ◽  
Zine El-Abdin Guennoun
Keyword(s):  
Cauchy Problem ◽  
Differential Inclusions ◽  
The Cauchy Problem
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