Abstract:
In this paper, we consider a weighted neutral functional differential equation of fractional order 0<α<1, with nonzero initial values, infinite delay, and the standard Riemann–Liouville fractional derivative. By using a variety of tools of fractional calculus including the Schauder fixed point theorem and the Banach fixed point theorem, we verify the existence, uniqueness and continuous dependence of solution of weighted neutral problem.
Keywords:
fractional functional differential equations, fractional derivative and fractional integral, existence and continuous dependence, fixed point theorem.
Received: 19.12.2017 Received in revised form: 24.05.2018 Accepted: 16.07.2018
Bibliographic databases:
Document Type:
Article
UDC:
517.9
Language: English
Citation:
Mohammed S. Abdo, Satish K. Panchal, “Weighted fractional neutral functional differential equations”, J. Sib. Fed. Univ. Math. Phys., 11:5 (2018), 535–549
This publication is cited in the following 14 articles:
Abdelhamid Moussaoui, Said Melliani, “Fixed point results under admissible α-η-F-simulation fuzzy contraction with application”, Int J Syst Assur Eng Manag, 2024
Fatima Zahra Arioui, “Weighted fractional stochastic integro-differential equation with infinite delay”, Arab. J. Math., 12:3 (2023), 499
Mohammed S. Abdo, Mohammed Zakarya, Emad E. Mahmoud, Saeed M. Ali, Abdel-Haleem Abdel-Aty, Yusuf Gurefe, “On
ψ
-Caputo Partial Hyperbolic Differential Equations with a Finite Delay”, Journal of Function Spaces, 2022 (2022), 1
Mohammed S. Abdo, “Qualitative Analyses of ψ-Caputo Type Fractional Integrodifferential Equations in Banach Spaces”, J. Adv. App. Comput. Math., 9 (2022), 1
A. S. Alnahdi, M. B. Jeelani, M. S. Abdo, S. M. Ali, S. Saleh, “On a nonlocal implicit problem under Atangana-Baleanu-Caputo fractional derivative”, Bound. Value Probl., 2021:1 (2021), 104
N. Adjimi, A. Boutiara, M. S. Abdo, M. Benbachir, “Existence results for nonlinear neutral generalized Caputo fractional differential equations”, J. Pseudo-Differ. Oper. Appl., 12:2 (2021), 25
M. S. Abdo, S. K. Panchal, “Initial value problem for a fractional neutral differential equation with infinite delay”, Int. J. Nonlinear Anal. Appl., 12:1 (2021), 1195–1206
A. Boutiara, M. S. Abdo, M. Benbachir, “Existence results for psi-Caputo fractional neutral functional integro-differential equations with finite delay”, Turk. J. Math., 44:6 (2020), 2380–2401
H. A. Wahash, M. S. Abdo, S. K. Panchal, “Existence and Ulam-Hyers stability of the implicit fractional boundary value problem with psi-Caputo fractional derivative”, J. Appl. Math. Comput. Mech., 19:1 (2020), 89–101
S.S. Redhwan, S.L. Shaikh, M.S. Abdo, S.Y. Al-Mayyahi, “Sadik transform and some result in fractional calculus”, Malaya J. Mat., 8:2 (2020), 536
Ufa Math. J., 11:4 (2019), 151–170
M. S. Abdo, S. K. Panchal, A. M. Saeed, “Fractional boundary value problem with psi-Caputo fractional derivative”, Proc. Indian Acad. Sci.-Math. Sci., 129:5 (2019), UNSP 65
H. A. Wahash, M. S. Abdo, S. K. Panchal, “An existence result for fractional integro-differential equations in Banach spaces”, J. Math. Ext., 13:3 (2019), 19–33
Abdo M.S., Wahash H.A., Panchal S.K., “Positive Solution of a Fractional Differential Equation With Integral Boundary Conditions”, J. Appl. Math. Comput. Mech., 17:3 (2018), 5–15
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