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

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DOI:

https://doi.org/10.26637/mjm502/005

Abstract

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 measure

Mathematics 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

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Published

01-04-2017

How to Cite

A. M. A. El-Sayed, M. SH. Mohamed, and K. M. O. Msaik. “On Two Boundary-Value Problems of Functional Integro-Differential Equations With Nonlocal Conditions”. Malaya Journal of Matematik, vol. 5, no. 02, Apr. 2017, pp. 265-71, doi:10.26637/mjm502/005.