On some analytic properties of tempered fractional calculus

DOI10.1016/j.cam.2019.112400zbMath1428.26012arXiv1912.05482OpenAlexW2967440696MaRDI QIDQ2332707

Arran Fernandez, Ceren Ustaoglu

Publication date: 5 November 2019

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.05482

zbMATH Keywords

hypergeometric functionsfractional calculusMellin transformsintegral inequalitiestempered fractional calculusTaylor theorem

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33)

Related Items (17)

Some inequalities for multiplicative tempered fractional integrals involving the \(\lambda \)-incomplete gamma functions ⋮ Some parameterized inequalities arising from the tempered fractional integrals involving the (μ,η)-incomplete gamma functions ⋮ Existence results of nonlinear generalized proportional fractional differential inclusions via the diagonalization technique ⋮ Generalized proportional fractional integral inequalities for convex functions ⋮ On the analytical development of incomplete Riemann–Liouville fractional calculus ⋮ On discrete tempered fractional calculus and its application ⋮ High-order spectral collocation method using tempered fractional Sturm-Liouville eigenproblems ⋮ ADI finite element Galerkin methods for two-dimensional tempered fractional integro-differential equations ⋮ A fast numerical solution of the <scp>3D</scp> nonlinear tempered fractional integrodifferential equation ⋮ Crank-Nicolson ADI finite difference/compact difference schemes for the 3D tempered integrodifferential equation associated with Brownian motion ⋮ Representation of solutions for Sturm–Liouville eigenvalue problems with generalized fractional derivative ⋮ On tempered fractional calculus with respect to functions and the associated fractional differential equations ⋮ Some new tempered fractional Pólya-Szegö and Chebyshev-type inequalities with respect to another function ⋮ Tempered and Hadamard-type fractional calculus with respect to functions ⋮ Certain Grüss-type inequalities via tempered fractional integrals concerning another function ⋮ Fast BDF2 ADI methods for the multi-dimensional tempered fractional integrodifferential equation of parabolic type ⋮ On tempered Hilfer fractional derivatives with respect to functions and the associated fractional differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• What is a fractional derivative?
• Tempered fractional calculus
• Some generating relations for extended hypergeometric functions via generalized fractional derivative operator
• Generalized Taylor's formula
• The mean value theorem and Taylor's theorem for fractional derivatives with Mittag-Leffler kernel
• A comparative study on generating function relations for generalized hypergeometric functions via generalized fractional operators
• Incomplete Caputo fractional derivative operators
• On fractional calculus with general analytic kernels
• On some new properties of fractional derivatives with Mittag-Leffler kernel
• Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions
• Well-posedness and numerical algorithm for the tempered fractional differential equations
• An extension of Caputo fractional derivative operator and its applications
• High Accuracy Algorithm for the Differential Equations Governing Anomalous Diffusion
• Generalized mittag-leffler function and generalized fractional calculus operators
• Decomposition of an Integral Operator by Use of Mikusiński Calculus
• Fractional Calculus
• On Generalized Gamma Functions Occurring in Diffraction Theory^*

This page was built for publication: On some analytic properties of tempered fractional calculus