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Using The Measure Of Noncompactness To Study A Nonlinear Impulsive Cauchy Problem With Two Different Kinds Of Delay

Author

Listed:
  • KAMAL SHAH

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia‡Department of Mathematics, University of Malakand, Chakdara Dir Lower 18000, Khyber Pakhtunkhwa, Pakistan)

  • NABIL MLAIKI

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia)

  • THABET ABDELJAWAD

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia†Department of Medical Research, China Medical University, Taichung 40402, Taiwan, R. O. China)

  • ARSHAD ALI

    (��Department of Mathematics, University of Malakand, Chakdara Dir Lower 18000, Khyber Pakhtunkhwa, Pakistan)

Abstract

We apply the noncompactness measure by Mawhin to establish sufficient conditions for the existence and uniqueness (EU) of solution to a nonlinear Cauchy problem. The aforesaid problem is investigated under impulsive and nonlinear integral boundary conditions. Further, the problem under consideration contains Caputo-type fractional-order derivative while two different kinds of delay are also involved. After establishing the existence results, we derive some adequate results for the stability analysis of Hyers–Ulam (HU) type. Here, it should be kept in mind that the proposed tools can reduce the strong compact condition by weaker compactness. For justification, we provide some examples also.

Suggested Citation

  • Kamal Shah & Nabil Mlaiki & Thabet Abdeljawad & Arshad Ali, 2022. "Using The Measure Of Noncompactness To Study A Nonlinear Impulsive Cauchy Problem With Two Different Kinds Of Delay," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(08), pages 1-14, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:08:n:s0218348x22402186
    DOI: 10.1142/S0218348X22402186
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