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Existence of Solutions for a Functional Integro-Differential Equation with Infinite Point and Integral Conditions

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Abstract

In this article, we study the existence of solutions for two initial value problems of the functional integro-differential equation with nonlocal infinite-point and integral conditions. We study the continuous dependence of the solution. As some examples illustrate the importance of the results.

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References

  1. Aikhazraji, A.S.A.: Traffic flow problem with differential equation. AL-Fatih J. 35, 38–46 (2008)

    Google Scholar 

  2. Coleman, C.S., Braun, M., Drew, D.A.: Differential Equation Models. Springer, Berlin (1983)

    Google Scholar 

  3. Deimling, K.: Nonlinear Functional Analysis. Springer, Berlin (1985)

    Book  Google Scholar 

  4. Dugundji, J., Granas, A.: Fixed Point Theory, Monografie Mathematyczne. PWN, Warsaw (1982)

    MATH  Google Scholar 

  5. El-Kadeky, KhW: A nonlocal proplem of the differential equation \(x^{\prime }= f(t, x, x^{\prime })\). J. Fract. Calc. Appl. 3(7), 1–8 (2012)

    Google Scholar 

  6. El-Owaidy, H., El-Sayed, A.M.A., Ahmed, R.G.: Existence of solutions of a coupled system of functional integro-differential equations of arbitrary (fractional) orders. Malaya J. Mat. 6(4), 774–780 (2018)

    Article  MathSciNet  Google Scholar 

  7. El-Sayed, A.M.A., Gamal, R.: Infinite point and riemann-stieltjes integral conditions for an integro-differential equation. Nonlinear Anal. Model. Control 24(4), 485–506 (2019)

  8. Ge, F., Zhou, H., Kou, C.: Existence of solutions for a coupled fractional differential equations with infinitely many points boundary conditions at resonance on an unbounded domain. Differ. Equ. Dyn. Syst. 24, 1–17 (2016)

    Article  MathSciNet  Google Scholar 

  9. Goebel, K., Kirk, W.A.: Topics in Metric Fixed Point Theory. Cambirdge Universty Press, Cambirdge (1990)

    Book  Google Scholar 

  10. Guo, L., Liu, L., Wu, Y.: Existence of positive solutions for singular fractional differential equations with infinite-point boundary conditions. Nonlinear Anal. Model. Control 21, 635–650 (2016)

    Article  MathSciNet  Google Scholar 

  11. Kolomogorov, A.N., Fomin, S.V.: Inroductory Real Analysis. Dover Publications Inc, New York (1975)

    Google Scholar 

  12. Liu, B., Li, J., Liu, L., Wang, Y.: Existence and uniqueness of nontrivial solutions to a system of fractional differential equations with riemann-stieltjes integral conditions. Adv. Differ. Equ. 2018(1), 306 (2018)

    Article  MathSciNet  Google Scholar 

  13. Liu, X., Liu, L., Wu, Y.: Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives. Bound. Value Probl. 2018(1), 24 (2018)

    Article  MathSciNet  Google Scholar 

  14. Marcellini, F.: Ode-pde models in traffic flow dynamics. Bull. Braz. Math. Soc. 47(1), 1–12 (2016)

    MathSciNet  MATH  Google Scholar 

  15. Min, D., Liu, L., Wu, Y.: Uniqueness of positive solutions for the singular fractional differential equations involving integral boundary value conditions. Bound. Value Probl. 2018(1), 23 (2018)

    Article  MathSciNet  Google Scholar 

  16. Srivastava, H.M., El-Sayed, A.M.A., Gaafar, F.M.: A class of nonlinear boundary value problems for an arbitrary fractional-order differential equation with the riemann-stieltjes functional integral and infinite-point boundary conditions. Symmetry 10(508), 1–13 (2018)

    Google Scholar 

  17. Zhang, X., Liu, L., Wu, Y., Zou, Y.: Existence and uniqueness of solutions for systems of fractional differential equations with riemann-stieltjes integral boundary condition. Adv. Differ. Equ. 2018(1), 204 (2018)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculty of Science, Alexandria University, Alexandria, Egypt

    A. M. A. El-Sayed

  2. Faculty of Science, Al-Azhar University, Cairo, Egypt

    Reda Gamal Ahmed

Authors
  1. A. M. A. El-Sayed
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  2. Reda Gamal Ahmed
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Correspondence to Reda Gamal Ahmed.

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El-Sayed, A.M.A., Ahmed, R.G. Existence of Solutions for a Functional Integro-Differential Equation with Infinite Point and Integral Conditions. Int. J. Appl. Comput. Math 5, 108 (2019). https://doi.org/10.1007/s40819-019-0691-2

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  • DOI: https://doi.org/10.1007/s40819-019-0691-2

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