Quasi-linear fractional differential equations with non-local condition
DOI: 10.54647/mathematics110482 58 Downloads 4848 Views
Author(s)
Abstract
In this paper, we study the existence of solutions for quasi-linear fractional differential equations with non-local condition using the Schauder fixed point theorem in Banach space. Later, we discuss a particular example which satisfies all the existence conditions.
Keywords
Quasi-linear fractional differential equations; Schauder fixed point; non-local condition
Cite this paper
Ala Eddine TAIER, Ranchao Wu,
Quasi-linear fractional differential equations with non-local condition
, SCIREA Journal of Mathematics.
Volume 9, Issue 2, April 2024 | PP. 46-56.
10.54647/mathematics110482
References
[ 1 ] | A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006. |
[ 2 ] | V. Lakshmikantham, S. Leela, J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009. |
[ 3 ] | K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equation, Wiley, New York,1993. |
[ 4 ] | I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, New York, 1999. |
[ 5 ] | S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993. |
[ 6 ] | D. Baleanu , K. Diethelm , E. Scalas , J.J. Trujillo , Fractional Calculus Models and Numerical Methods, in: Series on Complexity, Nonlinearity and Chaos, World Scientific, Boston, 2012 . |
[ 7 ] | X. Dong, Z. Bai, S. Zhang, Positive solutions to boundary value problems of p-laplacian with fractional derivative, Bound. Value Probl. 2017 (2017) 1-15. |
[ 8 ] | S. Das , Functional Fractional Calculus for System Identification and Controls, Springer, New York, 2008. |
[ 9 ] | D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, 2014. |
[ 10 ] | X. Zhao, F. An, The eigenvalues and sign-changing solutions of a fractional boundary value problem, Adv. Diff. Equa. 2016 (2016) 109. |
[ 11 ] | Z.M. Ge , C.Y. Ou , Chaos synchronization of fractional order modified duffing systems with parameters excited by a chaotic signal, Chaos Solitons Fractals 35 (2008) 705-717. |
[ 12 ] | J. Klafter , S.C. Lim , R. Metzler , Fractional Dynamics in Physics, World Scientific, Singapore, 2011 . |
[ 13 ] | R. Metzler , J. Klafter , The random walks guide to anomalous diffusion: a fractional dynamics approach, Phys. Rep. 339 (2000) 1-77 . |
[ 14 ] | M. Ostoja-Starzewski , Towards thermoelasticity of fractal media, J. Therm. Stress. 30 (2007) 889896. |
[ 15 ] | Y.Z. Povstenko , Fractional Thermoelasticity, Springer, New York, 2015 . |
[ 16 ] | Y. Pu, P. Siarry, J. Zhou, N. Zhang, A fractional partial differential equation based multiscale denoising model for texture image, Math. Methods Appl. Sci. 37 (2014) 1784-1806. |