TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Terminal value problem for impulsive fractional differential equation via Kuratowski measure of non-compactness

* ,

* Corresponding author · click or hover a name for details

pp. 1491–1504Vol. 27Issue 7November 2024DOI: 10.47974/JIM-1750XML
Received:
07 Dec 2022
Published Online:
30 Nov 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-1750
Pages:
1491–1504

Abstract

In this paper, we study the existence of solutions for terminal value problem for impulsive differential equation via ϴ-Riemann-Liouville fractional derivative in a appropriate Banach space. Our approach is based on Mönch fixed point theorem via Kuratowski measure of non-compactness, an example is given to illustrate our approach.

Keywords

Subject Classifications

(2010) 26A3334A6034A0834A37

References

[1] R. P. Agarwal, M. Meehan, D. O’Regan, Fixed Point Theory and Applications, Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge (2001).
[2] Z. Agur, L. Cojocaru, G. Mazaur, R. M. Anderson, Y. L. Danon, Pulse mass measles vaccination across age cohorts, Proc. Nat. Acad. Sci., 90, 11698-11702 (1993).
[3] J. BanaŚ, K. Goebel, Measures of noncompactness in Banach spaces, Lecture Note in Pure App. Math., 60, Dekker, New York (1980).
[4] M. Beddani, Solution set for impulsive fractional differential inclusions, Kragujevac. J. Math., 46 (1), 49-64 (2022).
[5] M. Beddani and B. Hedia, Existence result for a fractional differential equation involving a sequential derivative, Moroccan J. of Pure and Appl. Anal., 8 (1), 67-77 (2022).
[6] M. Beddani and B. Hedia, Existence result for fractional differential equations on unbounded domain, Kragujevac J. Math., 48 (5), 755-766 (2024).
[7] M. Benchohra, S. Bouriah and J. J. Nieto Terminal value problem for differential equations with Hilfer-Katugampola fractional derivative, Symmetry, 11, 675-389 (2019).
[8] M. Bezziou, Z. Dahmani and Ameth Ndiaye, Langevin differential equation of fractional order in non compactness Banach space, J. Interdiscip. Math., 23, 857-876 (2020).
[9] Q. Chen, A. Debbouche, Z. Luo and J. Wang, Impulsive fractional differential equations with Riemann-Liouville derivative and iterative learning control, Chaos Solitons Fractals, 102, 111-118 (2017).
[10] M. FeČkan, Y. Zhou and J. Wang, On the concept and existence of solution for impulsive fractional differential equations, Commun. Nonlinear Sci. Numer. Simul., 17, 3050-3060 (2012).
[11] L. Ghaffour and Z. Dahmani, Fractional differential equations with arbitrary singularities, Journal of Information and Optimization Sciences, 39, 1547-1565 (2018).
[12] D. J. Guo, V. Lakshmikantham, X. Liu, Nonlinear Integral Equations in Abstract Spaces, Kluwer Academic Publishers, Dordrecht (1996).
[13] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier B.V. Amsterdam (2006).
[14] D. Luo, J. R. Wang, M. Feckan, Applying fractional calculus to analyze economic growth modelling, J. Appl. Math. Stat. Inform., 14, 25-36 (2018).
[15] I. Podlubny, Fractional Differential Equations, in: Mathematics in Science and Engineering, vol. 198, Academic Press, New York, London, Toronto (1999).
[16] M. A. Ragusa, A. Razani, Weak solutions for a system of quasilinear elliptic equations, Contrib. Math., 1, 11-16 (2020).
[17] M. A. Ragusa, V. B. Shakhmurov, A Navier-Stokes-type problem with high-order elliptic operator and applications, Mathematics, 8 (12), 2256-2279 (2020).
[18] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon (1993).
[19] J. Vanterler da C. Sousa, E. Capelas de Oliveira, On the ϴ-Hilfer fractional derivative, Commun. Nonlinear Sci. Numer. Simul., 60, 72-91 (2018). 

Views: 236Downloads: 106Citations: 0