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February 28, 2026Fractal and Fractional0 citationsOpen Access

Rational Quasicontractions and Fractional Delayed Nonlocal Caputo Problems

Rational (a,p)-Quasicontractions and Fractional Delayed Nonlocal Caputo Problems via Hammerstein Operators

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Authors

MÖMahpeyker Öztürk

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Overview

Establishes fixed points in Banach spaces using rational quasicontractions, indicating new solutions for nonlinear boundary value problems.

Key Points

  • This research aims to introduce rational (a,p)−quasicontractions and explore their implications in fixed-point theory and Caputo fractional problems.
  • Introduced a new class of nonlinear operators called rational (a,p)−quasicontractions.
  • Established Greguš-type fixed-point theorems for closed convex subsets of Banach spaces.
  • Transformed a Caputo fractional differential equation with delay into a Hammerstein integral equation.
  • Applied natural growth and rational Lipschitz conditions to analyze the nonlocal problems.
  • Demonstrated the existence and uniqueness of fixed points for rational (a,p)−quasicontractions.
  • Validated convergence of the Picard iteration for initial guesses in the context of these operators.
  • Showed global attractivity of positive solutions for the associated boundary value problem.

Cite This Study

Mahpeyker Öztürk (2026) studied this question.

synapsesocial.com/papers/69a287460a974eb0d3c02ce7https://doi.org/10.3390/fractalfract10030148
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