On some boundary-value problems of functional integro-differential equations with nonlocal conditions

A. M. A. El-Sayed; M. SH. Mohamed; K. M. O. Msaik

doi:10.26637/mjm502/001

Abstract

In this paper, we study the existence of solution for some boundary value problems of functional integro-differential equations with nonlocal boundary conditions.

Keywords:

Nonlocal boundary value problems, Schauder fixed point theorem, functional integral equation, functional integro-differential equation, Lebesgue dominated convergence theorem

Mathematics Subject Classification:

534A08, 47H07, 47H10

Authors Imprint References Funding Related Articles Downloads

A. M. A. El-Sayed Faculty of Science, Alexandria University, Alexandria, Egypt. https://orcid.org/0000-0001-7092-7950
M. SH. Mohamed Faculty of Science, Alexandria University, Alexandria, Egypt.
K. M. O. Msaik Faculty of Education, Al Jabal al gharbi University, Al zintan, Libya.

Pages: 186-193
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.

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).

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.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.

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

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