Results 221 to 230 of about 8,551 (258)

On a generalization of the operators of fractional integration and differentiation

Applicable Analysis, 1992
Some general fractional integral operators are studied including those of RIEMANN-LIOUVILLE, HADAMARD and others. They are used to solve a generalized ABEL equation.
exaly   +2 more sources

On the integration of differential fractions

Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation, 2013
In this paper, we provide a differential algebra algorithm for integrating fractions of differential polynomials. It is not restricted to differential fractions that are the derivatives of other differential fractions. The algorithm leads to new techniques for representing differential fractions, which may help converting differential equations to ...
François Boulier, François Lemaire, Georg Regensburger, Markus Rosenkranz   +3 more
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Fractional pseudospectral integration matrices for solving fractional differential, integral, and integro-differential equations

Communications in Nonlinear Science and Numerical Simulation, 2016
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Xiaojun Tang, Heyong Xu
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Introduction to fractional integrability and differentiability

The European Physical Journal Special Topics, 2011
In this paper, we mainly consider fractional integral and derivatives including the Riemann-Liouville derivative, Caputo derivative, Grunwald-Letnikov derivative, Marchaud derivative, Riesz derivative, local fractional derivative, Canavati derivative. Then we introduce their existence conditions.
C.P. Li, Z.G. Zhao
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Basics on Fractional Differentiation and Integration

2020
Derivatives of orders of natural numbers have been widely known and commonly used since the origin of the calculus in the seventeenth century. On the other hand, derivatives whose orders are not necessarily natural numbers seem not to be well-known but have been considered since Leibniz (e.g., Ross [25]).
Adam Kubica, Katarzyna Ryszewska, Masahiro Yamamoto   +2 more
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Comparative study of fractional-order differentiators and integrators

2017 40th International Conference on Telecommunications and Signal Processing (TSP), 2017
The transfer function of fractional-order differentiators and integrators can be approximated through the utilization of appropriate integer-order transfer functions. Efficient tools towards this goal include the Continued Fraction Expansion as well as the Oustaloup's approximations.
Georgia Tsirimokou, Aslihan Kartci, Jaroslav Koton, Norbert Herencsar, Costas Psychalinos   +4 more
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On square integrable solutions of a fractional differential equation

Applied Mathematics and Computation, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ekin Ugurlu, Dumitru Baleanu, Kenan Tas
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Studies on fractional order differentiators and integrators: A survey

Signal Processing, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The construction of operational matrix of fractional integration for solving fractional differential and integro-differential equations

Neural Computing and Applications, 2017
This study intends to present a general formulation for the hybrid Jacobi and block pulse operational matrix of fractional integral operator in order to solve fractional differential and integro-differential equations. First, we define hybrid Jacobi polynomials and block pulse functions as an orthogonal basis for function approximation.
Farzane Yousefi, Azim Rivaz, Wen Chen 0003   +2 more
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Fuzzy fractional functional integral and differential equations

Fuzzy Sets and Systems, 2015
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