Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Science, University Badji Mokhtar Annaba, 23000 , Annaba, Algeria.

Abstract

This paper explores the study of a specific category of nonlinear multi-point boundary value problems (BVPs) associated with Riesz-Caputo fractional differential equations and integral boundary conditions. The primary objective is to establish the existence of solutions under specific assumptions. We use Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative to achieve this goal. Furthermore, numerical examples are presented and plotted to demonstrate the effectiveness of the obtained results.

Keywords

Main Subjects

1. B. Ahmad, S. K. Ntouyas and A. Alsaedi, Fractional order differential systems involving right Caputo and left Riemann-Liouville fractional derivatives with nonlocal coupled conditions. Bound. Value Probl. Berlin, 2019, 109.
2. R. L. Bagley and P. J. Torvik, A theoretical basis for the application of fractional calculus to viscoelasticity, J. Rheol. 27, 1983, pp. 201-210.
3. D. Baleanu, K. Diethelm, E. Scalas and J. Trujillo, Fractional Calculus: Models and Numerical Methods. 3, Series on Complexity, Nonlinearity and Chaos, World Scientific Publishing, Hackensack, (2012).
4. A. Carpinteri, P. Cornetti and A. Sapora, Nonlocal elasticity: an approach based on fractional calculus. Meccanica. 49,(2014), pp. 2551-2569.
5. F. Chen, D. Baleanu and GC. Wu, Existence results of fractional differential equations with Riesz–Caputo derivative. Eur. Phys. J. Spec. Top. Berlin. 226,(2017), pp. 3411-3425.
6. C.Y. Gu, J. Zhang and G.C. Wu, Positive solutions of fractional differential equations with the Riesz space derivative. Appl. Math. Lett. Oxford, 95 (2019), pp. 59-64.
7. M. Feng, X. Zhang and W. Ge, New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions. Bound. Value Probl. Berlin., 2011, pp 20.
8. A. Guezane-Lakoud and R. Khaldi, Solutions for a nonlinear fractional Euler–Lagrange type equation. SeMA J. Madrid, 76 (2019), pp. 195-202.
9. A. Guezane-Lakoud, R. Khaldi and A. Kılıçman, Existence of solutions for a mixed fractional boundary value problem. Adv. Difference Equ. Berlin, 2017, pp 164.
10. A. Guezane-Lakoud and R. Rodríguez-López, Positive solutions to mixed fractional p-Laplacian boundary value problems. J. Appl. Anal. Berlin, 29 (2023), pp. 49-58.
11. R. Hilfer, Ed., Applications of Fractional Calculus in Physics, World Scientific, River Edge, NJ, USA, 2000.
12. S. Jiang, J. Zhang, Q. Zhang, Z. Zhang, Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations. Commun. Comput. Phys., Hong Kong, 21 (2017), pp. 650-678.
13. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006).
14. S. Li, Z. Zhang, W. Jiang, Positive solutions for integral boundary value problems of fractional differential equations with delay. Adv. Difference Equ. Berlin, 2020, 256.
15. I. Merzoug, A. Guezane-Lakoud, R. Khaldi, Existence of solutions for a nonlinear fractional p-Laplacian boundary value problem. Rend. Circ. Mat. Palermo, II. Ser 69 (2020), pp. 1099-1106.
16. R. Khaldi, A. Guezane-Lakoud, On generalized nonlinear Euler-Bernoulli Beam type equations, Acta Univ. Sapientiae, Mathematica, Cluj-Napoca, 10 (2018), pp. 90-100.
17. R. Khaldi, A. Guezane-Lakoud, Higher order fractional boundary value problems for mixed type derivatives, Journal of Nonlinear Functional Analysis, Vol. 2017 , Article ID 30, pp. 1-9.
18. R. Khaldi., A. Guezane-Lakoud, On a generalized Lyapunov inequality for a mixed fractional boundary value problem, AIMS Mathematics, 2019, 4(3), pp. 506-515.
19. S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications. Switzerland: Gordon and Breach Science Publishers, 1993.
20. Q. Yang, F. Liu, I. Turner, Numerical methods for fractional partial differential equations with Riesz space fractional derivatives, Appl. Math. Model. Amsterdam, 34 (2010), pp. 200-218.