On some fractional order differential equations with weighted conditions
Downloads
DOI:
https://doi.org/10.26637/mjm1002/006Abstract
In this paper, we study some Cauchy problems with weighted conditions of a fractional order differential equation . We study by using some fixed point Theorems the existence of at least one solution in the two spaces $C_{1-\kappa}(I)$ and $C(I)$, where $I=[0,\hbar]$.
Keywords:
Fractional derivatives and integrals, Existence of solution, Cauchy problemMathematics Subject Classification:
26A33, 34A12, 47D09- Pages: 159-170
- Date Published: 16-02-2024
- Vol. 10 No. 02 (2022): Malaya Journal of Matematik (MJM)
A. M. A. EL-SAYEd And SH. A. ABD EL-SALAM, Weighted Cauchy-type problem of a functional differintegral equation, EJQTDE, $mathbf{3 0}(2007)$ 1-9.
A. M. A. El-SAyEd And Sh. A. ABd EL-SALAm, $L_p$ - solution of weighted Cauchy-type problem of a differ-integral functional equation, Inter. J. of Nonlinear Sci., 5(2008), 1-9.
A. M. A. El-Sayed And Sh. A. Abd El-Salam, Coupled system of a fractional order differential equations with weighted initial conditions, Open Math., 17(2019), 1737-1749.
F. M. GAAFAR, Cauchy-type problems of a functional differential equations with advanced arguments, Journal of Fractional Calculus and Applications, 5(2)(2014), 71-77.
I. M. Gelfand And G. E. Shilov, Generalized Functions, vol. 1, Fizmatgiz, Moscow, (1959) (in Russian).
K. M. Furati And N. E. TAtar, Long time behavior for a nonlinear fractional model, J. Math. Anal. Appl., 332(2007), 441-454.
K. M. FURATI AND N. E. TATAR, Power-type estimates for a nonlinear fractional differential equation, Nonlinear Analysis, 62(2005), 1025-1036.
K. M. Furati And N. E. TATAR, An existence results for a nonlocal fractional differential problem, Journal of Fractional Calculus, 26(2004), 43-51.
K. S. Miller And B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley, New York (1993).
I. Podlubny, Fractional Differential Equations, Acad. press, San Diego-New York-London (1999).
S. Samko, A. Kilbas And O. L. MariChev, Fractional Integrals and Derivatives, Gordon and Breach Science Publisher, (1993).
K. DeImling, Nonlinear Functional Analysis, Springer-Verlag, (1985).
- NA
Metrics
Published
Versions
- 16-02-2024 (3)
- 01-04-2022 (1)
How to Cite
Issue
Section
License
Copyright (c) 2022 Sheren Abd E L-SALAM
This work is licensed under a Creative Commons Attribution 4.0 International License.
