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Measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations

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  • Rabbani, Mohsen
  • Das, Anupam
  • Hazarika, Bipan
  • Arab, Reza

Abstract

The purpose of this article is to introduce a new tempered sequence space and obtain the measure of noncompactness in this space. Using the measure of noncompactness and generalized Darbo fixed point theorem, we discuss the existence of solutions of an infinite system of fractional differential equations. Also we provide an example to highlight and establish the importance of our main result. Finally, we approach the solution of the example with high accuracy, by a convergent iterative algorithm with the help of modified homotopy perturbation method.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306172
    DOI: 10.1016/j.chaos.2020.110221
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    References listed on IDEAS

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    1. Sadeghi, S. & Jafari, H. & Nemati, S., 2020. "Operational matrix for Atangana–Baleanu derivative based on Genocchi polynomials for solving FDEs," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Abu Arqub, Omar & Al-Smadi, Mohammed, 2018. "Atangana–Baleanu fractional approach to the solutions of Bagley–Torvik and Painlevé equations in Hilbert space," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 161-167.
    3. Mollapourasl, R. & Ostadi, A., 2015. "On solution of functional integral equation of fractional order," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 631-643.
    4. Rabbani, Mohsen & Arab, Reza & Hazarika, Bipan, 2019. "Solvability of nonlinear quadratic integral equation by using simulation type condensing operator and measure of noncompactness," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 102-117.
    5. M. Mursaleen & Abdullah Alotaibi, 2012. "Infinite System of Differential Equations in Some Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-20, November.
    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. 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).

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