Initial-value problem for a linear ordinary differential equation of noninteger order
Journal Article
·
· Sbornik. Mathematics
- Scientific Research Institute of Applied Mathematics and Automation, Kabardino-Balkar Scientific Centre of the Russian Academy of Sciences, Nalchik (Russian Federation)
An initial-value problem for a linear ordinary differential equation of noninteger order with Riemann-Liouville derivatives is stated and solved. The initial conditions of the problem ensure that (by contrast with the Cauchy problem) it is uniquely solvable for an arbitrary set of parameters specifying the orders of the derivatives involved in the equation; these conditions are necessary for the equation under consideration. The problem is reduced to an integral equation; an explicit representation of the solution in terms of the Wright function is constructed. As a consequence of these results, necessary and sufficient conditions for the solvability of the Cauchy problem are obtained. Bibliography: 7 titles.
- OSTI ID:
- 21592555
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 4 Vol. 202; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
Similar Records
Differential equations where the derivative is taken with respect to a measure
Boundary Value Problems for Nonclassical Systems of Second Order Differential Equations
The inverse scattering problem for a discrete Sturm-Liouville equation on the line
Journal Article
·
Sun Feb 27 23:00:00 EST 2011
· Sbornik. Mathematics
·
OSTI ID:21592564
Boundary Value Problems for Nonclassical Systems of Second Order Differential Equations
Journal Article
·
Sun Jan 14 23:00:00 EST 2018
· Journal of Mathematical Sciences
·
OSTI ID:22771602
The inverse scattering problem for a discrete Sturm-Liouville equation on the line
Journal Article
·
Sun Jul 31 00:00:00 EDT 2011
· Sbornik. Mathematics
·
OSTI ID:21592536