On the existence for impulsive fuzzy nonlinear integro-differential equations with nonlocal condition
Authors
N. H. M. Qumami
- School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded-431606, India.
R. S. Jain
- School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded-431606, India.
B. S. Reddy
- School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded-431606, India.
Abstract
This work is involved with first-order impulsive functional nonlinear fuzzy integro-differential equations with nonlocal condition in Banach space by using the concept of fuzzy numbers whose values are upper semicontinuous, normal, convex, and compact. The result is obtained by using the Leray-Schauder alternative fixed point theorem. Finally, an application is given that supports us to validate the result.
Share and Cite
ISRP Style
N. H. M. Qumami, R. S. Jain, B. S. Reddy, On the existence for impulsive fuzzy nonlinear integro-differential equations with nonlocal condition, Journal of Mathematics and Computer Science, 32 (2024), no. 1, 13--24
AMA Style
Qumami N. H. M., Jain R. S., Reddy B. S., On the existence for impulsive fuzzy nonlinear integro-differential equations with nonlocal condition. J Math Comput SCI-JM. (2024); 32(1):13--24
Chicago/Turabian Style
Qumami, N. H. M., Jain, R. S., Reddy, B. S.. "On the existence for impulsive fuzzy nonlinear integro-differential equations with nonlocal condition." Journal of Mathematics and Computer Science, 32, no. 1 (2024): 13--24
Keywords
- Nonlocal condition
- Leary-Schauder alternative fixed point theorem
- fuzzy nonlinear integro-differential equations
- mild solution
MSC
References
-
[1]
D. D. Bainov, S. G. Hristova, Integral inequalities of Gronwall type for piecewise continuous functions, J. Appl. Math. Stochastic Anal., 10 (1997), 89–94
-
[2]
M. Benchohra, J. Henderson, S. Ntouyas, Impulsive differential equations and inclusions, Hindawi Publishing Corporation, New York (2006)
-
[3]
M. Benchohra, J. J. Nieto, A. Ouahab, Fuzzy solutions for impulsive differential equations, Commun. Appl. Anal., 11 (2007), 379–394
-
[4]
M. A. Diallo, K. Ezzinbi, A. S´ene, Impulsive integro-differential equations with nonlocal conditions in Banach spaces, Trans. A. Razmadze Math. Inst., 171 (2017), 304–315
-
[5]
M. A. Diop, M. Dieye, H. Hmoyed, K. Ezzinbi, On the existence of mild solutions for nonlocal impulsive partial integrodifferential equations in Banach spaces, Le Matematiche, 74 (2019), 13–34
-
[6]
A. Granas, J. Dugundji, Fixed point theory, Springer-Verlag, New York (2003)
-
[7]
M. Guo, X. Xue, R. Li, Impulsive functional differential inclusions and fuzzy population models, Fuzzy Sets and Systems, 138 (2003), 601–615
-
[8]
X. Hao, L. Liu, Mild solution of semilinear impulsive integro-differential evolution equation in Banach spaces, Math. Methods Appl. Sci., 40 (2017), 4832–4841
-
[9]
R. S. Jain, M. B. Dhakne, On impulsive nonlocal integro-differential equations with finite delay, Int. J. Math. Res., 5 (2013), 361–373
-
[10]
S. D. Kadam, S. Reddy, R. Menon, R. S. Jain, Existence and controllability of mild solution of impulsive integro-differential equations inclusions, Nonlinear Funct. Anal. Appl., 25 (2020), 657–670
-
[11]
V. Lakshmikantham, F. A. Mcrae, Basic results for fuzzy impulsive differential equations, Math. Inequal. Appl., 4 (2001), 239–246
-
[12]
H.-Y. Lan, J. J. Nieto, On initial value problems for first-order implicit impulsive fuzzy differential equations, Dynam. Systems Appl., 18 (2009), 677–686
-
[13]
M. Mazandarani, M. Najariyan, Fuzzy differential equations: conceptual interpretations, Evol. Intell., (2022), 1–6
-
[14]
M. Mazandarani, L. Xiu, A review on fuzzy differential equations, IEEE Access, 9 (2021), 62195–62211
-
[15]
M. L. Puri, D. A. Ralescu, L. Zadeh, Fuzzy random variables, In: Readings in fuzzy sets for intelligent systems, Morgan Kaufmann, (1993), 265–271
-
[16]
R. Ramesh, S. Vengataasalam, Existence and uniqueness theorem for a solution of fuzzy impulsive differential equations, Ital. J. Pure Appl. Math., 33 (2014), 345–358
-
[17]
A. M. Samoilenko, N. A. Perestyuk, Impulsive differential equations, World Scientific Publishing Co., River Edge (1995)
-
[18]
S. Vengataasalam, R. Ramesh, Existence of fuzzy solutions for impulsive semilinear differential equations with nonlocal condition, Int. J. Pure. Appl. Math., 95 (2014), 297–308