Taylor's formula involving generalized fractional derivatives

DOI10.1016/j.amc.2018.04.040zbMath1427.26002arXiv1712.04630OpenAlexW2775361481MaRDI QIDQ2335574

Mondher Benjemaa

Publication date: 14 November 2019

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

Full work available at URL: https://arxiv.org/abs/1712.04630

zbMATH Keywords

fractional calculusTaylor formulaCaputo derivativesgeneralized fractional derivatives

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Fractional derivatives and integrals (26A33) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Fractional ordinary differential equations (34A08)

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Cites Work

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• Maximum principles for multi-term space-time variable-order fractional diffusion equations and their applications
• On the fractional signals and systems
• Fractional processes and fractional-order signal processing. Techniques and applications
• New approach to a generalized fractional integral
• On Caputo modification of the Hadamard fractional derivatives
• Generalized Taylor's formula
• Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability
• Fractional-order systems and controls. Fundamentals and applications
• Fractional dynamics. Applications of fractional calculus to dynamics of particles, fields and media
• Non-local continuum mechanics and fractional calculus
• On a Riemann-Liouville generalized Taylor's formula
• Time fractional quantum mechanics
• Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations
• Fractional differential equations of Caputo-Katugampola type and numerical solutions
• Completely monotone generalized Mittag-Leffler functions
• A class of time-fractional hemivariational inequalities with application to frictional contact problem
• The Cantor function
• And I say to myself: “What a fractional world!”
• Fractional diffusion and wave equations
• Applications of Fractional Calculus to the Theory of Viscoelasticity
• Muntz type Theorems I
• Muntz Systems and Orthogonal Muntz-Legendre Polynomials
• On the generalized fractional derivatives and their Caputo modification
• A New Approach to Generalized Fractional Derivatives
• Properties of the Katugampola fractional derivative with potential application in quantum mechanics
• Fractional Calculus
• Fractional Brownian Motions, Fractional Noises and Applications
• The random walk's guide to anomalous diffusion: A fractional dynamics approach