Properties of fractional calculus with respect to a function and Bernstein type polynomials

DOI10.1002/MMA.8557OpenAlexW4288758326MaRDI QIDQ6182027

Gastão S. F. Frederico, J. Vanterler da Costa Sousa, Edmundo Capelas de Oliveira, D. S. Oliveira

Publication date: 20 December 2023

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.8557

zbMATH Keywords

\(\psi\)-Hilfer fractional derivative\(\psi\)-Riemann-Liouville fractional integralfractional mean value theoremBernstein type polynomials

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Polynomials and matrices (11Cxx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Caputo-type modification of the Hadamard fractional derivatives
• Approximation of fractional integrals by means of derivatives
• A new formula for fractional integrals of Chebyshev polynomials: application for solving multi-term fractional differential equations
• Fractional-order nonlinear systems. Modeling, analysis and simulation
• A fast numerical algorithm based on the second kind Chebyshev polynomials for fractional integro-differential equations with weakly singular kernels
• \(\psi\)-Hilfer pseudo-fractional operator: new results about fractional calculus
• On some fractional generalizations of the Laguerre polynomials and the Kummer function
• On a Riemann-Liouville generalized Taylor's formula
• Laguerre polynomials of arbitrary (fractional) orders.
• A method for fractional Volterra integro-differential equations by Laguerre polynomials
• New operational matrix via Genocchi polynomials for solving Fredholm-Volterra fractional integro-differential equations
• A Caputo fractional derivative of a function with respect to another function
• The Laguerre-Hermite spectral methods for the time-fractional sub-diffusion equations on unbounded domains
• Caputo derivatives of fractional variable order: numerical approximations
• Leibniz type rule: \(\psi\)-Hilfer fractional operator
• On the \(\psi\)-Hilfer fractional derivative
• Expansion formula for fractional derivatives in variational problems
• Further properties of Osler's generalized fractional integrals and derivatives with respect to another function
• On the \(\Psi \)-fractional integral and applications
• Uniform approximation of fractional derivatives and integrals with application to fractional differential equations
• Numerical approximations of fractional derivatives with applications
• A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
• Approximate solution for system of fractional non-linear dynamical marriage model using Bernstein polynomials
• Fractional Calculus: Integral and Differential Equations of Fractional Order
• A numerical approach for solving weakly singular partial integro‐differential equations via two‐dimensional‐orthonormal Bernstein polynomials with the convergence analysis
• Fractional Calculus
• An Integral Equation Involving Legendre Functions
• The Fractional Derivative of a Composite Function
• Analysis of fractional differential equations

This page was built for publication: Properties of fractional calculus with respect to a function and Bernstein type polynomials