Search

The main crux of this work is to study the equivalence of modulus of smoothness and K-functionals in the Sobolev space W 2 , ν , M p constructed by the canonical Fourier–Bessel differential operator Δ ν M on the half-line where ν > - 1 / 2 and M ∈ S L (2 , R) . The proofs are based on harmonic analysis related to the generalized canonical Fourier–Bessel differential operator and its associated transform. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the existence of anti-periodic solutions for a nonlinear coupled system of Ψ - Caputo fractional differential equations with p - Laplacian operator in a Banach space. The proofs of our main results are based on Mönch's fixed point theorem and some basic tools of Ψ - Caputo fractional calculus paired with measures of noncompactness. As an application, our theoretical results have been illustrated by providing an interesting example. [ABSTRACT FROM AUTHOR]