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Applications of a new measure of noncompactness to the solvability of systems of nonlinear and fractional integral equations in the generalized Morrey spaces

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Abstract

This article introduces a measure of noncompactness in the generalized Morrey space. We study the applications of our new definition in investigating the conditions for the existence of solutions for systems of nonlinear integral equations. We can extend many useful theorems in \(L^{p}(\mathbb {R}^{N})\) for functions belonging to the generalized Morrey spaces. Compared to the \(L^{p}(\mathbb {R}^{N})\) spaces, the advantage of studying in the Morrey spaces is that we can research no compact support functions in our problems. Finally, significant examples are presented to show the efficiency of the main results.

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The authors have no relevant financial or non-financial interests to disclose and no funding was received to assist with the preparation of this manuscript.

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Authors and Affiliations

  1. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran

    Hengameh Tamimi, Somayeh Saiedinezhad & Mohammad Bagher Ghaemi

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  1. Hengameh Tamimi
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  2. Somayeh Saiedinezhad
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  3. Mohammad Bagher Ghaemi
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All authors contributed to the writing of this manuscript. Detailed designs of the problem were performed by S. Saiedinezhad and H. Tamimi. All authors read and approved the final manuscript.

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Correspondence to Somayeh Saiedinezhad.

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Tamimi, H., Saiedinezhad, S. & Ghaemi, M.B. Applications of a new measure of noncompactness to the solvability of systems of nonlinear and fractional integral equations in the generalized Morrey spaces. Fract Calc Appl Anal 27, 1215–1235 (2024). https://doi.org/10.1007/s13540-024-00262-8

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  • DOI: https://doi.org/10.1007/s13540-024-00262-8

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