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Integral equations of fractional order in Lebesgue spaces

  • Nickolai Kosmatov EMAIL logo
Published/Copyright: June 23, 2016
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 19 Issue 3

Abstract

We discuss solvability of a nonlinear Riemann-Liouville integral equation in Lebesgue spaces. We treat the Volterra equations of the first and the second types by applying boundedness criteria for the Riemann-Liouville integral operator. The existence of a solution to integral equations will follow from the Leray-Schauder Nonlinear Alternative.

Key Words and Phrases: Carathéodory conditions; Leray-Schauder Nonlinear Alternative; Riemann-Liouville derivative; Volterra integral equation
MSC 2010: Primary 34A34; Secondary 34A08; 34A12

Dedicated to Professor Stefan G. Samko on the occasion of his 75th anniversary

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Received: 2015-8-30
Published Online: 2016-6-23
Published in Print: 2016-6-1

© 2016 Diogenes Co., Sofia

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA-volume 19-3-2016)
  4. Survey Paper
  5. Fractional integrals and derivatives: mapping properties
  6. Research Paper
  7. Riesz fractional integrals in grand lebesgue spaces on ℝn
  8. Survey Paper
  9. United lattice fractional integro-differentiation
  10. Research Paper
  11. Integral equations of fractional order in Lebesgue spaces
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  13. General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems
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  15. Multilinear integral operators in weighted grand Lebesgue spaces
  16. Research Paper
  17. Fractional integration operator on some radial rays and intertwining for the Dunkl operator
  18. Research Paper
  19. Pseudo almost automorphy of semilinear fractional differential equations in Banach Spaces
  20. Research Paper
  21. Existence and uniqueness of global solutions of caputo-type fractional differential equations
  22. Research Paper
  23. Perfect nonlinear observers of fractional descriptor continuous-time nonlinear systems
https://doi.org/10.1515/fca-2016-0035
Keywords for this article
Carathéodory conditions; Leray-Schauder Nonlinear Alternative; Riemann-Liouville derivative; Volterra integral equation

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA-volume 19-3-2016)
  4. Survey Paper
  5. Fractional integrals and derivatives: mapping properties
  6. Research Paper
  7. Riesz fractional integrals in grand lebesgue spaces on ℝn
  8. Survey Paper
  9. United lattice fractional integro-differentiation
  10. Research Paper
  11. Integral equations of fractional order in Lebesgue spaces
  12. Research Paper
  13. General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems
  14. Research Paper
  15. Multilinear integral operators in weighted grand Lebesgue spaces
  16. Research Paper
  17. Fractional integration operator on some radial rays and intertwining for the Dunkl operator
  18. Research Paper
  19. Pseudo almost automorphy of semilinear fractional differential equations in Banach Spaces
  20. Research Paper
  21. Existence and uniqueness of global solutions of caputo-type fractional differential equations
  22. Research Paper
  23. Perfect nonlinear observers of fractional descriptor continuous-time nonlinear systems
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