On Boundary Value Problems with Implicit Random Non-Conformable Fractional Differential Equations
DOI:
https://doi.org/10.5644/SJM.19.02.08Keywords:
Implicit differential equations, non conformable fractional derivative, existence, random solution, Ulam stability, fixed pointAbstract
In this paper, we present some results on the existence, uniqueness and Ulam stability for a class of problems for nonlinear implicit random fractional differential equations with non-conformable derivatives. For our proofs, we employ some suitable fixed point theorems. Finally, we provide some illustrative examples.
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S. Abbas, M. Benchohra, J. R. Graef, J. Henderson, Implicit Fractional Differential and Integral Equations: Existence and Stability, de Gruyter, Berlin, 2018.
S. Abbas, M. Benchohra, G. M. N'Guérékata, Topics in Fractional Differential Equations. Springer, New York, 2012.
S. Abbas, M. Benchohra and G. M. N'Guérékata, Advanced Fractional Differential and Integral Equations, Nova Science Publishers, New York, 2015.
T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics. 279 (2015), 57-66.
F. Bekada, S. Abbas, and M. Benchohra, Boundary value problem for Caputo-Fabrizio random fractional differential equations, Moroccan J. Pure Appl. Anal. (MJPAA) 6 (2) (2020), 218-230.
F. Bekada, S. Abbas, M. Benchohra, and J. J. Nieto, Dynamics and stability for Katugampola random fractional differential equations, AIMS Mathematics. (2021), 8654-8666.
N. Benkhettou, K. Aissani, A. Salim, M. Benchohra and C. Tunc, Controllability of fractional integro-differential equations with infinite delay and non-instantaneous impulses, Appl. Anal. Optim. 6 (2022), 79-94.
M. Benchohra, F. Bouazzaoui, E. Karapinar and A. Salim, Controllability of second order functional random differential equations with delay, Math. 10 (2022), 16pp. https://doi.org/10.3390/math10071120
C. Derbazi, H. Hammouche, A. Salim and M. Benchohra, Measure of noncompactness and fractional Hybrid differential equations with Hybrid conditions, Differ. Equ. Appl. 14 (2022), 145-161. http://dx.doi.org/10.7153/dea-2022-14-09
H. W. Engl, A general stochastic fixed-point theorem for continuous random operators on stochastic domains, Anal. Appl. 66 (1978), 220-231.
P. M. Guzman, G. Langton, L. L. Motta, J. Medina and J. E. Napoles V., A New definition of a fractional derivative of local type, J. Math. Anal. 9 (2018), 88-98.
A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.
S. Itoh, Random fixed point theorems with applications to random differential equations in Banach spaces, J. Math. Anal. Appl. 67 (1979), 261-273.
A. Heris, A. Salim, M. Benchohra and E. Karapinar, Fractional partial random differential equations with infinite delay, Results in Physics. (2022). https://doi.org/10.1016/j.rinp.2022.105557
R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264 (2014), 65-70.
S. Krim, A. Salim, S. Abbas and M. Benchohra, On implicit impulsive conformable fractional differential equations with infinite delay in $b$-metric spaces, Rend. Circ. Mat. Palermo (2). (2022), 1-14. https://doi.org/10.1007/s12215-022-00818-8
N. Laledj, A. Salim, J. E. Lazreg, S. Abbas, B. Ahmad and M. Benchohra, On implicit fractional $q$-difference equations: Analysis and stability, Methods Appl. Sci. 45 (17) (2022), 10775-10797. https://doi.org/10.1002/mma.8417
J. E. Napoles V., P. M. Guzman and L. M. Lugo, Some new results on nonconformable fractional calculus, Advances in Dynamical Systems and Applications, 13 (2018), 167-175.
A. Salim, S. Abbas, M. Benchohra and E. Karapinar, Global stability results for Volterra-Hadamard random partial fractional integral equations, Rend. Circ. Mat. Palermo (2), (2022), 1-13. https://doi.org/10.1007/s12215-022-00770-7
A. Salim, M. Benchohra, J. R. Graef and J. E. Lazreg, Initial value problem for hybrid $psi$-Hilfer fractional implicit differential equations, J. Fixed Point Theory Appl. 24 (2022), 14 pp. https://doi.org/10.1007/s11784-021-00920-x
A. Salim, J. E. Lazreg, B. Ahmad, M. Benchohra and J. J. Nieto, A study on $k$-generalized $psi$-Hilfer derivative operator, Vietnam J. Math. (2022). https://doi.org/10.1007/s10013-022-00561-8
A. Salim, F. Mesri, M. Benchohra and C. Tunç, Controllability of second order semilinear random differential equations in Fréchet spaces, Mediterr. J. Math. 20 (84) (2023), 1-12. https://doi.org/10.1007/s00009-023-02299-0
S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Amsterdam, 1987, Engl. Trans. from the Russian.
O. Tunç and C. Tunç, Solution estimates to Caputo proportional fractional derivative delay integro-differential equations, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat} 117 (2023), 12. https://doi.org/10.1007/s13398-022-01345-y
O. Tunç and C. Tunç, Ulam stabilities of nonlinear iterative integro-differential equations, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117 (2023), 118. https://doi.org/10.1007/s13398-023-01450-6
