Abstract ordinary and fractional neural network approximations based on Richard’s curve.- Abstract Multivariate Neural Network Approximation based on Richard’s curve.- Parametrized hyperbolic tangent based Banach space valued basic and fractional neural network approximations.- Parametrized hyperbolic tangent induced Banach space valued multivariate multi layer neural network approximations.- Banach space valued neural network approximation based on a parametrized arctangent sigmoid function.- Parametrized arctangent activated Banach space valued multi layer neural network multivariate approximation.- Banach space valued Ordinary and Fractional neural networks approximations based on the parametrized Gudermannian function.- Parametrized Gudermannian activation function based Banach space valued neural network multivariate approximation.- Banach space valued univariate neural network approximation based on parametrized error activation function.- Banach space valued multivariate multi layer neural network approximation based on parametrized error activation function.- Hyperbolic Tangent Like based univariate Banach space valued neural network approximation.- Banach space valued neural network multivariate approximation based on hyperbolic tangent like activation function.- Banach space valued ordinary and fractional neural network approximations based on q-deformed hyperbolic tangent activation function.- Banach space valued multivariate multi layer neural network approximation based on q-deformed hyperbolic tangent activation function.- Banach space valued multivariate multi layer neural network approximation based on q-deformed and λ-parametrized A-generalized logistic function.- Banach space valued ordinary and fractional neural network approximation based on q-deformed and λ-parametrized A-generalized logistic function.- Banach space valued multivariate multi layer neural network approximation based on q-deformed and λ-parametrized hyperbolic tangent function.- q-Deformed and λ-parametrized hyperbolic tangent based Banach space valued ordinary and fractional neural network approximation.- Banach space valued multivariate multi layer neural network approximation based on q-Deformed and parametrized half hyperbolic tangent.- Banach space valued ordinary and fractional neural network approximation based on q-deformed and β-parametrized half hyperbolic tangent.- General sigmoid relied Banach space valued neural network approximation.- General sigmoid induced Banach space valued neural network multivariate approximation.- Fuzzy basic and fractional general sigmoid function generated neural network approximation.- Multivariate Fuzzy Approximation by Neural Network Operators induced by a general sigmoid function.- Multivariate Fuzzy-Random and stochastic general sigmoid activation function generated Neural Network Approximations.- Voronovskaya type asymptotic expansions for general sigmoid functions induced quasi-interpolation neural network operators.- Multiple general sigmoids activated Banach space valued neural network multivariate approximation.- Quantitative Approximation by Multiple sigmoids KantorovichChoquet quasi-interpolation neural network operators.- Degree of Approximation by Multiple sigmoids KantorovichShilkret quasi-interpolation neural network operators.- Approximation by Neural Networks of Brownian Motion.- Neural Networks Approximation of Time Separating Stochastic Processes.- Fractional Calculus between Banach spaces together with Ostrowski and Gr¨uss kind of inequalities.- Sequential Fractional Calculus between Banach spaces and corresponding Ostrowski and Gr¨uss kind of inequalities.