On two boundary-value problems of functional integro-differential equations with nonlocal conditions
Downloads
DOI:
https://doi.org/10.26637/mjm502/005Abstract
In this paper we establish the existence of solution for two boundary value problems of Fredholm functional integro-differential equations with nonlocal boundary conditions.
Keywords:
Nonlocal boundary value problems, Fredholm functional integral equation, Fredholm functional integro-differential equation, compact in measureMathematics Subject Classification:
534A08, 47H07, 47H10- Pages: 265-271
- Date Published: 01-04-2017
- Vol. 5 No. 02 (2017): Malaya Journal of Matematik (MJM)
P.B Bailey ,L.E. Shampine, P.E. Waltman, Nonlinear Two Point Boundary Value Problem, Academic Press, 1968.
J. Banas and Z. Knap, Integrable solutions of a functional-integral equation, Rev. Mat. Univ. Complut. Madrid 2 (1989), 31-38. DOI: https://doi.org/10.5209/rev_REMA.1989.v2.n1.18145
J. Banas, Integrable solutions of Hammerstein and Urysohn integral equations, J. Aust. Math. Soc. Ser A $46(1989) 61-68$. DOI: https://doi.org/10.1017/S1446788700030378
F.S. De Blasi, On a property of the unit sphere in a Banach space, Bull. Math. Soc. Sci. Math. R.S. Roumanie $21(1977), 259-262$.
A. Boucherif and Radu Precup, On the nonlocal IVP for first order differential equations, fixed point theory,Vol. 4, No.2, (2003), PP. 205-212.
A. Cafiada, P. Drabek and A. Fonda Handbook of differential equations, A survey , university of looannina, department of Mathematics, (2005).
J. Dugundji, and A. Grans, Fixed point theory, monografie mathematyczne, PWN, Warsaw (1963).
A.M.A. El-Sayed, Nonlinear functional differential equations of arbitrary orders, Nonlinear Anal. 33 (2) (1998) 181-186. DOI: https://doi.org/10.1016/S0362-546X(97)00525-7
A.M.A. El-Sayed, Fractional differential-difference equations, J. Fract. Calc. 10 (1996) 101-107.
A.M.A El-sayed , E . O Bin Taher, Positive solution for a nonlocal buondary-value proplem of class of arbitrary (fractional) orders differential equations. International Journal of Nonlinear Science. Vol.14(2012) No.4,pp.398- 404
A.M.A El-Sayed and Elkadeky, Kh. W, Caratheodory theorem for a nonlocal problem of The differential equation $x^{prime}=fleft(t, x^{prime}right)^{prime}$, Alexandria journal of Mathematics, (2010).
A.M.A El-Sayed, E.M. Hamdallah and Elkadeky, Kh. w, Uniformly stable positive monotonic solution of a nonlocal cauchy problem, Advances in pure Mathematics, Vol. 2, (2012), No.2, PP. 109-113 DOI: https://doi.org/10.4236/apm.2012.22015
A. M. A. El-Sayed and E. O. Bin-Taher, Positive nondecreasing solutions for a multi-term fractional-order functional differential equation with integral conditions, Electronic Journal of differential equations, Vol. 2011, ISSN 1072-6691, No. 166, (2011), PP. 1-8.
A. M. A. El-Sayed and E. O. Bin-Taher, a multi-term fractional-order differential equation with nonlocal condition, Egy. Chin.J Comp. App. Math., Vol. 1, No. 1, (2012), PP. 54-60.
G. Emmanuele, Integrable solutions of Hammerstien integral equations, Appl. Anal. 50 (3-4) (1993) 277284. DOI: https://doi.org/10.1080/00036819308840198
M. N. Gaston, A Cauchy problem for some fractional abstract differential equation with nonlocal conditions, Nonlinear Analysis, Vol. 70, (2009), pp. 1873-1876. DOI: https://doi.org/10.1016/j.na.2008.02.087
K. Goebel, and W. A. Kirk, Topics in metric fixed point theory, Cambridge University Press, Cambridge $(1990)$. DOI: https://doi.org/10.1017/CBO9780511526152
Gupta , C. P., Ntouyas, S. K. and Tsamatos , P. Ch. Solvability of an m-point boundary value problem for second order ordinary differential equations,J. Math. Anal. Appl., 189 (1995): 575-584. DOI: https://doi.org/10.1006/jmaa.1995.1036
A. N. Kolmogorov and S. V. Fomin, Itroductory real analysis Dover Publ. Inc 1975.
B. Liu, Existence and uniqueness of solutions to first order multi-point boundary value problems, Applied Mathematics Letters, Vol. 17, (2004), PP. 1307-1316. DOI: https://doi.org/10.1016/j.aml.2003.08.014
O. Nica, Initial value problem for first-order differential systems with general nonlocal condition, Electronic Journal of differential equations, Vol. 2012, No. 74, (2012), PP. 1-15.
Ma, R. Existence theorems for a second order m-point boundary value problem,J. Math. Anal. Appl., 211 (1997): 545-555. DOI: https://doi.org/10.1006/jmaa.1997.5416
- NA
Similar Articles
- John M. Rassias, M. Arunkumar, N. Mahesh Kumar , General solution and generalized Ulam-Hyers stability of a generalized 3-Dimensional AQCQ functional equation , Malaya Journal of Matematik: Vol. 5 No. 01 (2017): Malaya Journal of Matematik (MJM)
- Sandra Pinelas, M. Arunkumar, T. Namachivayam, E. Sathya, General solution and two methods of generalized Ulam - Hyers stability of n-dimensional AQCQ functional equation , Malaya Journal of Matematik: Vol. 5 No. 02 (2017): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2017 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.