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- Title
NON-AUTONOMOUS FRACTIONAL EVOLUTION EQUATIONS WITH NON-INSTANTANEOUS IMPULSE CONDITIONS OF ORDER (1,2): A CAUCHY PROBLEM.
- Authors
IQBAL, NAVEED; NIAZI, AZMAT ULLAH KHAN; KHAN, IKRAM ULLAH; KARACA, YELİZ
- 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.
- Subjects
EVOLUTION equations; CAUCHY problem; PARTIAL differential equations; FRACTIONAL calculus; PROBABILITY density function; INITIAL value problems
- Publication
Fractals, 2022, Vol 30, Issue 9, p1
- ISSN
0218-348X
- Publication type
Article
- DOI
10.1142/S0218348X22501961