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Solvability of Some Nonlinear Integral Functional Equations

Received: 11 February 2017     Accepted: 15 February 2017     Published: 28 February 2017
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Abstract

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.

Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 5-1)

This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics

DOI 10.11648/j.ajtas.s.2017060501.13
Page(s) 13-22
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Superposition Operator, Carathe'odory Conditions, Measure of Noncompactness, Fixed Point Theorem

References
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[2] J. Banas ́ and W. G. El-Sayed, Solvability of functional and Integral Equations in some of Classes integrable functions, (1993).
[3] J. Banas ́, and K. Goebel, Measures of noncompactness in Banach spaces, Lect. Notes in Math. 60, M. Dekker, New York and Basel, 1980.
[4] 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.
[5] G. Darbo, Punti Uniti in trasformazioni a codominio noncompatto, Rend. Sem. Mat. Univ, Padova, 24 (1955), 84-92.
[6] 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).
[7] 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.
[8] 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.
[9] 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.
[10] 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.
[11] 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.
[12] 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.
[13] 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.
[14] 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.
[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.
[16] 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.
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Cite This Article
  • APA Style

    Mahmoud M. El-Borai, Wagdy G. El-Sayed, Noura N. Khalefa. (2017). Solvability of Some Nonlinear Integral Functional Equations. American Journal of Theoretical and Applied Statistics, 6(5-1), 13-22. https://doi.org/10.11648/j.ajtas.s.2017060501.13

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    ACS Style

    Mahmoud M. El-Borai; Wagdy G. El-Sayed; Noura N. Khalefa. Solvability of Some Nonlinear Integral Functional Equations. Am. J. Theor. Appl. Stat. 2017, 6(5-1), 13-22. doi: 10.11648/j.ajtas.s.2017060501.13

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    AMA Style

    Mahmoud M. El-Borai, Wagdy G. El-Sayed, Noura N. Khalefa. Solvability of Some Nonlinear Integral Functional Equations. Am J Theor Appl Stat. 2017;6(5-1):13-22. doi: 10.11648/j.ajtas.s.2017060501.13

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  • @article{10.11648/j.ajtas.s.2017060501.13,
      author = {Mahmoud M. El-Borai and Wagdy G. El-Sayed and Noura N. Khalefa},
      title = {Solvability of Some Nonlinear Integral Functional Equations},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {6},
      number = {5-1},
      pages = {13-22},
      doi = {10.11648/j.ajtas.s.2017060501.13},
      url = {https://doi.org/10.11648/j.ajtas.s.2017060501.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2017060501.13},
      abstract = {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.},
     year = {2017}
    }
    

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    T1  - Solvability of Some Nonlinear Integral Functional Equations
    AU  - Mahmoud M. El-Borai
    AU  - Wagdy G. El-Sayed
    AU  - Noura N. Khalefa
    Y1  - 2017/02/28
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ajtas.s.2017060501.13
    DO  - 10.11648/j.ajtas.s.2017060501.13
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
    SP  - 13
    EP  - 22
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.s.2017060501.13
    AB  - 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.
    VL  - 6
    IS  - 5-1
    ER  - 

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Author Information
  • Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

  • Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

  • Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

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