Vallée-Poussin theorem for fractional functional differential equations with integral boundary condition

Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava

Research output: Contribution to journalArticlepeer-review

Abstract

This research paper focuses on the study of a Riemann-Liouville fractional functional differential equation and a linear continuous operator acting from the space of continuous functions to the space of essentially bounded functions with a boundary condition involving integral terms. We investigates the solvability and uniqueness of the equation under certain conditions on the coefficients. The paper utilizes techniques of Vallée-Poussin theorem, and Green’s function sign constancy to establish the main results. Choosing a corresponding function within the context of the Vallée-Poussin theorem results in explicit criteria presented as algebraic inequalities. These inequalities, as we illustrate through examples, cannot be further improved.

Original languageEnglish
JournalIndian Journal of Pure and Applied Mathematics
DOIs
StateAccepted/In press - 2024

Keywords

  • 34K10
  • 34K37
  • 34K38
  • 34K40
  • Boundary value problems
  • Differential inequality
  • Fractional differential equations
  • Riemann-Liouville derivative
  • Sign constancy of Green’s function

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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