On the Monotonic Solutions of Quadratic Integral Equations in Orlicz Space

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Amira M. Abdalla
Hussein A. H. Salem

Abstract

In this paper, Darbo's and Rothe's xed point theorems is used to prove the existence of monotonic solutions for the nonlinear quadratic fractional order integral equation of the following type x(t) = h(t) + Gx(t)Jα a(t)f(H1x(t),H2x(t)), t ∈ [1, e], α > 0, where a belongs to appropriate Orlicz space. Here Jα stands the Hadamard-type fractional integral operator.

Keywords:
Fractional calculus, quadratic integral equations, Orlicz spaces.

Article Details

How to Cite
M. Abdalla, A., & A. H. Salem, H. (2019). On the Monotonic Solutions of Quadratic Integral Equations in Orlicz Space. Journal of Advances in Mathematics and Computer Science, 30(5), 1-11. https://doi.org/10.9734/JAMCS/2019/46641
Section
Original Research Article