Some Aspects of Initial Value Problems Theory for Differential Equations with Riemann–Liouville Derivatives

Some Aspects of Initial Value Problems Theory for Differential Equations with Riemann–Liouville Derivatives

Some subjects of the well-formed initial value problems for ordinary differential equations with Riemann–Liouville derivatives are discussed. As an example the simplest linear homogeneous differential equation with two fractional derivatives is cited. It's shown, that the requirement of the hig...

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Main Author: E. N. Ogorodnikov
Format: Article
Language:English
Published: Samara State Technical University 2010-06-01
Series:Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
Online Access:http://mi.mathnet.ru/eng/vsgtu812
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spelling doaj-ef241f3bbb5e417aad0498e22f98fb592020-11-25T01:41:18ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812010-06-015(21)102310.14498/vsgtu812Some Aspects of Initial Value Problems Theory for Differential Equations with Riemann–Liouville DerivativesE. N. OgorodnikovSome subjects of the well-formed initial value problems for ordinary differential equations with Riemann–Liouville derivatives are discussed. As an example the simplest linear homogeneous differential equation with two fractional derivatives is cited. It's shown, that the requirement of the highest derivative summability influence the value of the lowest derivative order or the initial values in Cauchy type conditions. The specific class of functions, allowing the non-summability of the highest derivative, is introduced. The correctness of the modified Cauchy type problem and initial value problems with local and nonlocal conditions is substantiated.http://mi.mathnet.ru/eng/vsgtu812
collection DOAJ
language English
format Article
sources DOAJ
author E. N. Ogorodnikov
spellingShingle E. N. Ogorodnikov
Some Aspects of Initial Value Problems Theory for Differential Equations with Riemann–Liouville Derivatives
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
author_facet E. N. Ogorodnikov
author_sort E. N. Ogorodnikov
title Some Aspects of Initial Value Problems Theory for Differential Equations with Riemann–Liouville Derivatives
title_short Some Aspects of Initial Value Problems Theory for Differential Equations with Riemann–Liouville Derivatives
title_full Some Aspects of Initial Value Problems Theory for Differential Equations with Riemann–Liouville Derivatives
title_fullStr Some Aspects of Initial Value Problems Theory for Differential Equations with Riemann–Liouville Derivatives
title_full_unstemmed Some Aspects of Initial Value Problems Theory for Differential Equations with Riemann–Liouville Derivatives
title_sort some aspects of initial value problems theory for differential equations with riemann–liouville derivatives
publisher Samara State Technical University
series Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
issn 1991-8615
2310-7081
publishDate 2010-06-01
description Some subjects of the well-formed initial value problems for ordinary differential equations with Riemann–Liouville derivatives are discussed. As an example the simplest linear homogeneous differential equation with two fractional derivatives is cited. It's shown, that the requirement of the highest derivative summability influence the value of the lowest derivative order or the initial values in Cauchy type conditions. The specific class of functions, allowing the non-summability of the highest derivative, is introduced. The correctness of the modified Cauchy type problem and initial value problems with local and nonlocal conditions is substantiated.
url http://mi.mathnet.ru/eng/vsgtu812
work_keys_str_mv AT enogorodnikov someaspectsofinitialvalueproblemstheoryfordifferentialequationswithriemannliouvillederivatives
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