Research article

Monotonic solutions for a quadratic integral equation of fractional order

  • Received: 18 April 2019 Accepted: 30 June 2019 Published: 16 July 2019
  • In this paper we present a global existence theorem of a positive monotonic integrable solution for the mixed type nonlinear quadratic integral equation of fractional order $ x(t) = p(t) + h(t, x(t)) \int_{0}^{t} k(t, s)( f_1( s, I^\alpha f_2(s, x(s)))+g_1( s, I^\beta g_2(s, x(s)))) ds, ~t\in [0, 1], \alpha, \beta \gt 0 $ by applying the technique of measures of weak noncompactness. As an application, we consider an initial value problem of arbitrary (fractional) order differential equations.

    Citation: A. M. A. El-Sayed, Sh. M. Al-Issa. Monotonic solutions for a quadratic integral equation of fractional order[J]. AIMS Mathematics, 2019, 4(3): 821-830. doi: 10.3934/math.2019.3.821

    Related Papers:

  • In this paper we present a global existence theorem of a positive monotonic integrable solution for the mixed type nonlinear quadratic integral equation of fractional order $ x(t) = p(t) + h(t, x(t)) \int_{0}^{t} k(t, s)( f_1( s, I^\alpha f_2(s, x(s)))+g_1( s, I^\beta g_2(s, x(s)))) ds, ~t\in [0, 1], \alpha, \beta \gt 0 $ by applying the technique of measures of weak noncompactness. As an application, we consider an initial value problem of arbitrary (fractional) order differential equations.


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