Skip to main content
SpringerLink
Log in

On the Similarity between Volterra Operators and Transformation Operators for Integro-Differential Operators of Fractional Order

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

We establish the similarity between certain Volterra integral operators and the Riemann--Liouville fractional integration operator as well as the existence of a triangular transformation operator for integro-differential equations of fractional order. The results obtained are consistent with similar results for the case of integer order.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. L. A. Sakhnovich, “Reduction of Volterra operators to simplest form and inverse problems,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 21 (1957), no. 2, 235–262.

    Google Scholar 

  2. L. A. Sakhnovich, “The inverse problem for differential operators of order \(n > 2\) with analytic coefficients,” Mat. Sb. [Math. USSR-Sb.], 46 (1958), no. 1, 61–76.

    Google Scholar 

  3. I. G. Khachatryan, “On transformation operators for differential equations of higher orders,” Izv. Akad. Nauk Armyan. SSR Ser. Mat. 13 (1978), no. 3, 215–238.

    Google Scholar 

  4. O. V. Sedin, “On the similarity between the Volterra operator of \(n\)th degree and the integration operator,” in: Linear Operators in Function Spaces [in Russian], Groznyi, 1989.

  5. V. I. Matsaev, “On the existence of a transformation operator for differential operators of higher orders,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 130 (1960), no. 3, 499–502.

    Google Scholar 

  6. M. M. Malamud, “Similarity between Volterra operators and contiguous problems in the theory of differential equations of fractional order,” Trudy Moskov. Mat. Obshch. [Trans. Moscow Math. Soc.], 55 (1994), 73–148.

    Google Scholar 

  7. V. A. Ditkin and A. P. Prudnikov, Operational Calculus in Two Variables and its Applications [in Russian], Fizmatgiz, Moscow, 1958.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. N. G. Chernyshevskii Saratov State University, Russia

    M. Yu. Ignat'ev

Authors
  1. M. Yu. Ignat'ev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ignat'ev, M.Y. On the Similarity between Volterra Operators and Transformation Operators for Integro-Differential Operators of Fractional Order. Mathematical Notes 73, 192–201 (2003). https://doi.org/10.1023/A:1022154908077

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022154908077

Search

Navigation