Boundary value problems for nonlinear fractional differential equations with $\psi$-Caputo fractional
Résumé
In this present paper, we will envisaged the existence and uniqueness of solutions for the following boundary value problem for a nonlinear fractional differential equation involving with $\psi$-Caputo fractional derivative. Our results are proved under Banach contraction principle and Krasnoselkii's fixed point theorem.Téléchargements
Références
R. Almeida, A Caputo fractional derivative of a function with respect to another function,Nonlinear Science and Numerical Simulation, 44 (2017), 460–481.
R. Almeida, A.B. Malinowska, M.M.T. Monteiro, Fractional differential equations with a Caputo derivative with respect to a kernel function and their applications, Math. Meth. Appl, 41(2018), 336–352.
Z. Baitiche, C. Derbazi, M. Benchohra, -Caputo fractional differential equations with multi-point boundary conditions by topological degree theory, RNA, 3 (2020), 167–178.
A. Benlabess, M. Benbachir and M. Lakrib, Boundary value problems for nonlinear fractional differential equations, 30 (2015), 157–168.
I. Podlubny, Fractional differential equations, Mathematics in science and engineering, 198 (1999), 41–119.
D. Baleanu, H. Jafari, H. Khan and S. J. Johnston, Results for mild solution for fractional coupled hybrid boundary value problem. Open math, 13 (2005), 601–608.
D. Baleanu, H. Jafari, H. Khan and R.A. Alipour, On existence results for solutions of a coupled system of hybrid boundary value problems with hybrid conditions, Adv. Differ. Equ, 1 (2015), 1–14.
V. Daftardar-Gejji, Fractional calculus and fractional differential equations. Springer Nature Singapore, 2019.
B. C. Dhage, On −condensing mappings in Banach algebras, Math Student, 63 (1994), 146–152.
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