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An existence result for Hadamard type two dimensional fractional functional integral equations via measure of noncompactness

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  • Deep, Amar
  • Deepmala,
  • Hazarika, Bipan

Abstract

In this article, we investigate the existence of solutions for Hadamard type two dimensional fractional functional integral equations on [1,b]×[1,c]. We use the concept of measure of non-compactness and Darbo’s fixed point theorem as the main tool to prove our results. Also, with the help of an example, we discuss the validity of our result.

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  • Deep, Amar & Deepmala, & Hazarika, Bipan, 2021. "An existence result for Hadamard type two dimensional fractional functional integral equations via measure of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921002277
    DOI: 10.1016/j.chaos.2021.110874
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    References listed on IDEAS

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    1. Rabbani, Mohsen & Das, Anupam & Hazarika, Bipan & Arab, Reza, 2020. "Measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R., 2020. "Results on the existence and controllability of fractional integro-differential system of order 1 < r < 2 via measure of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Sen, Mausumi & Saha, Dipankar & Agarwal, R.P., 2019. "A Darbo fixed point theory approach towards the existence of a functional integral equation in a Banach algebra," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 111-118.
    4. Deep, Amar & Deepmala, & Rabbani, Mohsen, 2021. "A numerical method for solvability of some non-linear functional integral equations," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    5. Kavitha, K. & Vijayakumar, V. & Udhayakumar, R., 2020. "Results on controllability of Hilfer fractional neutral differential equations with infinite delay via measures of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Hazarika, Bipan & Srivastava, H.M. & Arab, Reza & Rabbani, Mohsen, 2019. "Application of simulation function and measure of noncompactness for solvability of nonlinear functional integral equations and introduction to an iteration algorithm to find solution," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 131-146.
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    Cited by:

    1. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy, 2021. "A note on approximate controllability for nonlocal fractional evolution stochastic integrodifferential inclusions of order r∈(1,2) with delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

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