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Existence of Solutions for a Class of Fredholm Integral–Differential Equations Via Measure of Noncompactness

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Abstract

In this present paper, we introduce a measure of noncompactness on the space \(C^{n} [a,b]\). As an application, we study the problem of existence of solutions of Fredholm integral–differential equations using the technique of measures of noncompactness in conjunction with Darbo’s fixed point theorem. Further, we give some illustrative examples to verify the effectiveness and applicability of our results.

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Authors and Affiliations

  1. Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

    R. Allahyari

  2. Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran

    R. Arab & A. Shole Haghigh

Authors
  1. R. Allahyari
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  2. R. Arab
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  3. A. Shole Haghigh
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Correspondence to R. Arab.

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Allahyari, R., Arab, R. & Shole Haghigh, A. Existence of Solutions for a Class of Fredholm Integral–Differential Equations Via Measure of Noncompactness. Iran J Sci Technol Trans Sci 41, 481–487 (2017). https://doi.org/10.1007/s40995-017-0250-9

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  • DOI: https://doi.org/10.1007/s40995-017-0250-9

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