On the nonlocal noninstataneous Impulsive Integro-differential equations in the frame of a fractional Caputo type derivative
DIOP, M., GARBA, C., BODJRENOU, F., Ezzinbi, K. (2025). On the nonlocal noninstataneous Impulsive Integro-differential equations in the frame of a fractional Caputo type derivative. EKB Journal Management System, 16(2), 1-18. doi: 10.21608/jfca.2025.317042.1126
Mamadou Abdoul DIOP; Chaibou Bakar GARBA; Firmin BODJRENOU; Khalil Ezzinbi. "On the nonlocal noninstataneous Impulsive Integro-differential equations in the frame of a fractional Caputo type derivative". EKB Journal Management System, 16, 2, 2025, 1-18. doi: 10.21608/jfca.2025.317042.1126
DIOP, M., GARBA, C., BODJRENOU, F., Ezzinbi, K. (2025). 'On the nonlocal noninstataneous Impulsive Integro-differential equations in the frame of a fractional Caputo type derivative', EKB Journal Management System, 16(2), pp. 1-18. doi: 10.21608/jfca.2025.317042.1126
DIOP, M., GARBA, C., BODJRENOU, F., Ezzinbi, K. On the nonlocal noninstataneous Impulsive Integro-differential equations in the frame of a fractional Caputo type derivative. EKB Journal Management System, 2025; 16(2): 1-18. doi: 10.21608/jfca.2025.317042.1126

On the nonlocal noninstataneous Impulsive Integro-differential equations in the frame of a fractional Caputo type derivative

Journal of Fractional Calculus and Applications
Volume 16, Issue 2, 2025, Page 1-18  XML PDF (475.01 K)
Document Type: Regular research papers
DOI: 10.21608/jfca.2025.317042.1126
View on SCiNiTO View on SCiNiTO
Authors
Mamadou Abdoul DIOP email 1; Chaibou Bakar GARBA2; Firmin BODJRENOU3; Khalil Ezzinbi4
1Department of Mathematics, Gaston Berger University, Sénégal
2Department of Mathematics, Gaston Berger University
3Institute of Mathematics and Physical Sciences, URMPM P.O. Box 613, Porto Novo, Benin
4Faculty of Sciences Semlalia, Department of Mathematics, Cadi Ayyad University, Marrakesh, Morocco.
Abstract
Study of evolution equations subjected to impulsive action, which starts abruptly and stays active on a finite time interval, has been a subject of interest in the last few years due to its applicability in practical problems. The pioneering work of such a model, known as non-instantaneous impulsive differential equation, is reported in the work of Hernandez and O’Regan \cite{Hernan}. The concept of resolvent operator is precisely relevant to dealing
integro-differential equations in Banach spaces. This strategy
has been utilized to a substantial type of nonlinear differential equations in Banach spaces.
For more points of interest on this concept, we refer to Grimmer\cite{R.GRIMMER}.
In this work, we investigate the existence of mild solutions for semilinear integro-differential systems in Banach spaces. Using M\"onch's fixed point theorem, the theory of Grimmer's resolvent operator and the measures of non compactness, we prove the main results of this work. At the end, an example is given to further illustrate the conclusions drawn from the theoretical study.
Keywords
Fractional integrodifferential equations; Resolvent Operator; Non-instantaneous impulse; Measure of non-compactness; M\"onch fixed point theorem
Statistics
Article View: 128
PDF Download: 161