On the Monotonic Solutions of Quadratic Integral Equations in Orlicz Space
Amira M. Abdalla *
Department of Mathematics and Computer Science, Faculty of Sciences, Alexandria University, Alexandria, Egypt.
Hussein A. H. Salem
Department of Mathematics and Computer Science, Faculty of Sciences, Alexandria University, Alexandria, Egypt.
*Author to whom correspondence should be addressed.
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.