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Hadamard Fractional Differential Equations on an Unbounded Domain with Integro-initial Conditions

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Abstract

In this paper, we introduce and investigate a Hadamard-type fractional differential equation on the interval \((1, \infty )\) equipped with a new class of logarithmic type integro-initial conditions. We apply the Leggett–Williams fixed point theorem and the concept of iterative positive solutions to establish the existence of solutions for the problem at hand. Our results are new and enrich the literature on Hadamard-type fractional differential equations on the infinite domain. Examples illustrating the main results are presented.

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Acknowledgements

The authors thank the anonymous referees for their valuable comments on their work that led to the improvement of the original manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Razi University, 67149, Kermanshah, Iran

    Nemat Nyamoradi

  2. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Bashir Ahmad

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  1. Nemat Nyamoradi
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  2. Bashir Ahmad
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N.N. and B.A. prepared the main manuscript text. The authors reviewed the manuscript.

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Correspondence to Nemat Nyamoradi.

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Nyamoradi, N., Ahmad, B. Hadamard Fractional Differential Equations on an Unbounded Domain with Integro-initial Conditions. Qual. Theory Dyn. Syst. 23, 183 (2024). https://doi.org/10.1007/s12346-024-01044-6

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