Constrained Problem of a Non Local Integral Problem of an Arbitrary Orders Differential Equation Subject to a Weighted Problem of a Delayed Fractional Differential Equation Constraint

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DOI: https://doi.org/10.28924/2291-8639-24-2026-141
Published: Apr 30, 2026
Cite as:
Hanadi Zahed, Ahmed M. A. El-Sayed, Eman M. A. Hamdallah, Amna B. Humieda, Constrained Problem of a Non Local Integral Problem of an Arbitrary Orders Differential Equation Subject to a Weighted Problem of a Delayed Fractional Differential Equation Constraint, Int. J. Anal. Appl., 24 (2026), 141.

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Hanadi Zahed, Ahmed M. A. El-Sayed, Eman M. A. Hamdallah, Amna B. Humieda

Abstract

This work presents a comprehensive theoretical framework proposing the existence of solution and its main properties of a constrained problem of an arbitrary orders differential equation with nonlocal-integral condition subject to a weighted problem of a delayed Riemann-Liouville fractional differential equation constraint. Firstly, we prove the existence of at least integrable solution of the constraint, then we prove that for every solution of the constraint there exists a unique continuous solution of the constrained problem it self. Moreover, examining the continuous dependence of the obtained solutions on some parameters and functions ensures the stability of the problem and establishes the existence and uniqueness of solutions. The Hyers–Ulam stability of the system is thoroughly analyzed, showing the strength of solutions against small perturbations in initial conditions or system parameters. The study develops comprehensive mathematical results based on the fixed point theorems in suitable spaces. We also deliver an example to demonstrate the validity of the theoretical findings and their potential application to dynamical systems and control problems.

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