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Zaid Laadjal

Publications and source records attributed to Zaid Laadjal.

3 recordsLinked to original sources
arXiv2026

Lyapunov-type inequality for fractional BVPs involving two Hadamard fractional derivatives of different orders

This paper establishes a Lyapunov-type inequality for a class of fractional boundary value problems (BVPs) involving two Hadamard fractional derivatives of different orders with Dirichlet boundary conditions. The method is based on the construction of the corresponding Green's function and establishing its maximum value through rigorous analytical techniques. The obtained inequality provides the necessary conditions for the existence of nontrivial solutions to the proposed problem. Finally, we illustrate the applicability of our results by establishing nonexistence criteria for nontrivial solutions to certain problems and providing examples.

math.GM↗
arXiv2020

Sharp estimates for the unique solution of the Hadamard-type two-point fractional boundary value problems

In this short note, we present the sharp estimate for the existence of a unique solution for a Hadamard-type fractional differential equations with two-point boundary value conditions. The method of analysis is obtained by using the integral of the Green's function and the Banach contraction principle. Further, we will also obtain a sharper lower bound of the eigenvalues for an eigenvalue problem. Two examples are presented to clarify the applicability of the essential results.

math.GM↗