NON-AUTONOMOUS FRACTIONAL EVOLUTION EQUATIONS WITH NON-INSTANTANEOUS IMPULSE CONDITIONS OF ORDER (1,2): A CAUCHY PROBLEM

Naveed Iqbal (), Azmat Ullah Khan Niazi (), Ikram Ullah Khan () and Yelä°z Karaca
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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

FRACTALS (fractals), 2022, vol. 30, issue 09, 1-16

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.

Keywords: Measure of Noncompactness (MNC); Non-autonomous Fractional Evolution Equations (NAFEE); Non-instantaneous Impulse Condition; Mixed-Type Integro-Differential Equations; Initial Value Problem (IVP); Mild Solution; Analytic Semigroup (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501961

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