<p>This paper presents Lyapunov-type inequalities for Caputo–Hadamard fractional differential equations with multi-point and integral boundary conditions (BCs). These inequalities provide new tools for analyzing the qualitative properties of solutions in fractional calculus. The results address a gap in the literature, where such inequalities under generalized BCs, especially integral constraints, have been rarely studied. The approach involves establishing precise kernel estimates and deriving separate Lyapunov-type bounds for problems with multi-point and integral BCs. An illustrative example is included to demonstrate the applicability and effectiveness of the results.</p>

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Unified approach to Lyapunov-type inequalities for Caputo–Hadamard fractional differential equations

  • Muralee Bala Krushna Boddu,
  • Ramakrishna Balireddy,
  • Veera Paparao Alla

摘要

This paper presents Lyapunov-type inequalities for Caputo–Hadamard fractional differential equations with multi-point and integral boundary conditions (BCs). These inequalities provide new tools for analyzing the qualitative properties of solutions in fractional calculus. The results address a gap in the literature, where such inequalities under generalized BCs, especially integral constraints, have been rarely studied. The approach involves establishing precise kernel estimates and deriving separate Lyapunov-type bounds for problems with multi-point and integral BCs. An illustrative example is included to demonstrate the applicability and effectiveness of the results.