American Journal of Theoretical and Applied Statistics
Volume 6, Issue 5-1, September 2017, Pages: 13-22
Received: Feb. 11, 2017;
Accepted: Feb. 15, 2017;
Published: Feb. 28, 2017
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Mahmoud M. El-Borai, Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt
Wagdy G. El-Sayed, Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt
Noura N. Khalefa, Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt
This paper discussed some existence theorems for nonlinear functional integral equations in the space L^1 of Lebesgue integrable functions,by using the Darbo fixed point theorem associated with the Hausdorff measure of noncompactness. Also, as an application, we discuss the existence of solutions for some nonlinear integral equations with fractional order.
Mahmoud M. El-Borai,
Wagdy G. El-Sayed,
Noura N. Khalefa,
Solvability of Some Nonlinear Integral Functional Equations, American Journal of Theoretical and Applied Statistics. Special Issue: Statistical Distributions and Modeling in Applied Mathematics.
Vol. 6, No. 5-1,
2017, pp. 13-22.
J. Appell, and P. P. Zabrejko, Continuity properties of the superposition operator, Preprint No. 131, Univ. Augsburg, 1986.
J. Banas ́ and W. G. El-Sayed, Solvability of functional and Integral Equations in some of Classes integrable functions, (1993).
J. Banas ́, and K. Goebel, Measures of noncompactness in Banach spaces, Lect. Notes in Math. 60, M. Dekker, New York and Basel, 1980.
Cance ́s and B. Mennucci, New applications of integral equations methods, for solving Continuum models: ionic solutions and liquid crystals, J. Math-chem, 23 (1998), 309-326.
G. Darbo, Punti Uniti in trasformazioni a codominio noncompatto, Rend. Sem. Mat. Univ, Padova, 24 (1955), 84-92.
M. M. EL-Borai, W. G. El-Sayed, E. HamdAllah and A. A. El- Shorbagy, on some partial Differential equations with operator coefficients and non-local conditions, life Science J. 2013; 10 (4), (3333-3336).
M. M. El-Borai, W. G. El-Sayed and A. M. Moter, Continuous Solutions of a Quadratic Integral Equation, Inter. J. Life Science and Math. (IJLSM), Vol. 2, (5)-4, (2015), 21-30.
M. M. El-Borai, W. G. El-Sayed. and R. M. Al-Masroub, Exact Solutions for Some Nonlinear Fractional Parabolic Equations, Inter. J. Adv. Eng. Res (IJAER), Vlo. 10, No. III, Sep. 2015, 106 – 122.
M. M. El-Borai, W. G. El-Sayed and A. M. Jawad, Adomian Decomposition Method for Solving Fractional Differtential Equations, Inter. Res. J. Eng. and Tech. (IRJET), Vol. 2, Iss. 6, 2015, 296-306.
M. M. El-Borai, W. G. El-Sayed and R. M. Al-Masroub, Exact Solutions for Time Fractional Coupled Whithambroer-Kaup Equations via exp-Function Method, Inter. Res. J. Eng. and Tech. (IRJET), Vol. 2, Iss. 6, 2015, 307-315.
M. M. El-Boraie, W. G. El-Sayed & R. M. Al-Masroub, Exact solutions of some nonlinear Complex fractional partial differential equations, Inter. J. Math. Tre & Tech. (IJMTT)- Vol. 32, No. 1, April (2016), 4-9.
M. M. El-Borai, W. G. El-Sayed and F. N. Ghaffoori, On the Cauchy problem for Some parabolic fractional partial differential equationswith time delays, J. Math. & System, Scie, 6 (2016)194-199.
M. M. El-Borai, W. G. El-Sayed and F. N. Ghaffoori, On the solvability of nonlinear integral functional equation, Inter. J. Math. Tren & Tech. (IJMTT), Vol. 34, No. 1 June 2016, 39-44.
M. M. El-Borai, W. G. El-Sayed and F. N. Ghaffoori, Existence Solution for a fractional Nonlinear Integral Equation of Volterra Type, Aryabhatta J. M & Inform, Vol. 08, Iss.-02, (Jul.-Dec. 2016), 1-15.
M. M. El-Borai, W. G-El-Sayed & R. M. Al-Masroubn, Exact Solutions of Some Nonlinear Partial Differential Equations via Extended (G'/G)-Expansion Method, Inter. J. Math. Trends And Tech. (IJMTT) – Vol. 36, No. 1- Aug. 2016, 60-71.
M. M. El-Borai, W. G. El-Sayed and M. I. Abbas, Monotonic solutions of some singular Integral equations of Volterra type, J. Studia (SMH), Scientiarum Mathematic arum Hungrica, 46 (3), (2009), 297-316.
W. G. El-Sayed, Nonlinear functional integral equations of convolution type, Portugaliae, Math, Vol. 54 Fasc. 4-1997.
J. Krzyz, On monotonicity-preserving transformation, Ann. Univ. Mariae Curie-klodowska, Sect. A, 6 (1952), 91-111.
W. RUDIN, Real and complex analysis, McGraw-Hill, New York, 1966.
P. P. Zabrejko, A. I. Koshelev, M. A. Krasnosel’skii, S. G. Mikhlin, L. S. Rakovshchik and V. J. Stecenko, Integral equations, Noordhoff, Leyden (1975).