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Non-Autonomous Fractional Evolution Equations With Non-Instantaneous Impulse Conditions Of Order (1,2): A Cauchy Problem

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Listed:
  • NAVEED IQBAL

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • AZMAT ULLAH KHAN NIAZI

    (Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan)

  • IKRAM ULLAH KHAN

    (Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan)

  • YELÄ°Z KARACA

    (University of Massachusetts Chan Medical School (UMASS), 55 Lake Avenue North, Worcester, MA 01655, USA4Massachusetts Institute of Technology (MIT), 77 Massachusetts Avenue, Cambridge, MA 02139, USA)

Abstract

The non-instantaneous condition is utilized in our study through the employment of the Cauchy problem in order to contract a system of nonlinear non-autonomous mixed-type integro-differential (ID) fractional evolution equations in infinite-dimensional Banach spaces. We reveal the existence of new mild solutions in the condition that the nonlinear function modifies approximately suitable, measure of non-compactness (MNC) form and local growth form using evolution classes along with fractional calculus (FC) theory as well as the fixed-point theorem with respect to k-set-contractive operator and MNC standard set. Consequently, as an example, we consider a fractional non-autonomous partial differential equation (PDE) with a homogeneous Dirichlet boundary condition and a non-instantaneous impulse condition. The conclusion of mild solution regarding the uniqueness and existence of a mild solution for a system with a probability density function and evolution classes is drawn with respect to the related domains.

Suggested Citation

  • Naveed Iqbal & Azmat Ullah Khan Niazi & Ikram Ullah Khan & Yelä°Z Karaca, 2022. "Non-Autonomous Fractional Evolution Equations With Non-Instantaneous Impulse Conditions Of Order (1,2): A Cauchy Problem," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(09), pages 1-16, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:09:n:s0218348x22501961
    DOI: 10.1142/S0218348X22501961
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