On a fractional integral equation of periodic functions involving Weyl–Riesz operator in Banach algebras

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Numerical Study of Fractional Differential Equations of Lane-Emden Type by Method of Collocation (2012, background): “Many studies on fractional calculus and fractional differential equations, involving different operators such as Riemann-Liouville operators [18], Erdlyi-Kober operators [19], Weyl-Riesz operators [20], Caputo operators [21] and Grnwald- Letnikov operators [22], have appeared during the past three d”
A NEW APPROACH TO GENERALIZED FRACTIONAL DERIVATIVES (2011, unknown): “nn-Liouville derivative of order α corresponds to the type β = 0, while the Caputo derivative to the type β = 1. The Weyl-Riesz fractional integration operator of a periodic function f takes the form [44], Wα = 1 2π Z2π 0 Ψα(τ)f(x −τ)dτ, where Ψα(τ) = 2 X∞ n=1 cosnτ nα , and 0 ≤ τ ≤ 2π. Further prop”
GENERALIZED ULAM-HYERS STABILITY FOR FRACTIONAL DIFFERENTIAL EQUATIONS (2012, background): “Many studies on fractional calculus and fractional differential equations, involving different operators such as Riemann–Liouville operators [3], Erdlyi–Kober operators [12], Weyl–Riesz operators [16], Caputo operators [2] and Grnwald–Letnikov operators [17], have appeared during the past three deca”