The STUDY ON CONFORMABLE FRACTIONAL NEUTRAL EVOLUTION EQUATIONS WITH NONLOCAL-DELAY CONDITIONS
Conformable Fractional neutral evolution equations with nonlocal-delay conditions
Resumo
This work is concerned with the study a class of conformable fractional neutral evolution equations with nonlocal-delay conditions. We prove the existence and uniqueness of mild solutions, by using some assymptions and applying the fixed point theorem and contraction mapping principal. In the end, we
give an example of applications.
Downloads
Não há dados estatísticos.
Referências
1. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983
2. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amesterdam, Netherlands, 2006.
3. A.M.A. El-Sayed, Fractional order diffusion-wave equations, Internat. J. Theoret. Phys. 35 (1996) 311-322.
4. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, CA, USA,( 1999).
5. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, New York, NY, USA, 1993.
6. L. Byszewski, Theorems about existence and uniqueness of solutions of a semi-linear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991) 494-505.
7. L. Byszewski, V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal. 40 (1991) 11-19.
8. M. Bouaouid, K. Hilal, and S. Melliani, Existence of mild solutions for conformable-fractional differential equations with non local conditions, Rocky Mountain Journal of Mathematics, https://projecteuclid.org/euclid.rmjm/1573354832, (2019).
9. P. Chen, X. Zhang, and Y. Li, Fractional non-autonomous evolution equation with nonlocal conditions, Journal of Pseudo-Differential Operators and Applications, vol. 10, no. 4, pp. 955-973, 2019.
10. P. Chen, X. Zhang, and Y. Li, Study on fractional non-autonomous evolution equations with delay, Computers and Mathematics with Applications, vol. 73, no. 5,(2017) pp. 794-803,.
11. R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics, vol. 264,(2014) pp. 65-70.,
12. T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics, vol. 279,(2015) pp. 57-66,.
13. X. Fu, K. Ezzinbi, Existence of solutions for neutral differential evolution equations with nonlocal conditions, Nonlinear Anal. 54 (2003) 215-227.
14. Zhou, Yong, and Feng Jiao. ”Existence of mild solutions for fractional neutral evolution equations.” Computers and Mathematics with Applications 59.3 (2010): 1063-1077.
2. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amesterdam, Netherlands, 2006.
3. A.M.A. El-Sayed, Fractional order diffusion-wave equations, Internat. J. Theoret. Phys. 35 (1996) 311-322.
4. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, CA, USA,( 1999).
5. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, New York, NY, USA, 1993.
6. L. Byszewski, Theorems about existence and uniqueness of solutions of a semi-linear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991) 494-505.
7. L. Byszewski, V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal. 40 (1991) 11-19.
8. M. Bouaouid, K. Hilal, and S. Melliani, Existence of mild solutions for conformable-fractional differential equations with non local conditions, Rocky Mountain Journal of Mathematics, https://projecteuclid.org/euclid.rmjm/1573354832, (2019).
9. P. Chen, X. Zhang, and Y. Li, Fractional non-autonomous evolution equation with nonlocal conditions, Journal of Pseudo-Differential Operators and Applications, vol. 10, no. 4, pp. 955-973, 2019.
10. P. Chen, X. Zhang, and Y. Li, Study on fractional non-autonomous evolution equations with delay, Computers and Mathematics with Applications, vol. 73, no. 5,(2017) pp. 794-803,.
11. R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics, vol. 264,(2014) pp. 65-70.,
12. T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics, vol. 279,(2015) pp. 57-66,.
13. X. Fu, K. Ezzinbi, Existence of solutions for neutral differential evolution equations with nonlocal conditions, Nonlinear Anal. 54 (2003) 215-227.
14. Zhou, Yong, and Feng Jiao. ”Existence of mild solutions for fractional neutral evolution equations.” Computers and Mathematics with Applications 59.3 (2010): 1063-1077.
Publicado
2025-09-26
Edição
Seção
Artigos
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
