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An Integral Equation Involving Legendre Functions [PDF]
, 1964 Rodrigues’s formula can be applied also to (1.1) and (1.3) but here the situation is slightly more involved in that the integrals with respect to σ^2 are of fractional order and their inversion requires the knowledge of differentiation and integration of
Erdélyi, A.
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Fractional Differential Equations [PDF]
International Journal of Differential Equations, 2010 1 School of Mathematical Sciences, Queensland University of Technology, P.O. Box 2434, Brisbane, Qeensland 4001, Australia 2 Department of Statistics and Probability, Michigan State University, A416 Wells Hall, East Lansing, MI 48823, USA 3 Department of Mathematics, Mu'tah University, P.O.
Fawang Liu +5 more
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Algorithms, 2018 This paper analyses algorithms currently found in the literature for the approximation of fractional order models and based on recursive pole and zero distributions.
Jocelyn Sabatier
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Fractional Sturm-Liouville eigenvalue problems, II [PDF]
, 2017 We continue the study of a non self-adjoint fractional three-term Sturm-Liouville boundary value problem (with a potential term) formed by the composition of a left Caputo and left-Riemann-Liouville fractional integral under {\it Dirichlet type} boundary
Dehghan, Mohammad, Mingarelli, Angelo B.
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A fractional B-spline collocation method for the numerical solution of fractional predator-prey models [PDF]
, 2018 We present a collocation method based on fractional B-splines for the solution of fractional differential problems. The key-idea is to use the space generated by the fractional B-splines, i.e., piecewise polynomials of noninteger degree, as approximating
Pitolli, Francesca
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Fractional order differentiation by integration with Jacobi polynomials [PDF]
, 2012 The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of ...
Gibaru, Olivier +3 more
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A New Class of Fractional Cumulative Residual Entropy - Some Theoretical Results
Journal of Telecommunications and Information Technology, 2023 In this paper, by differentiating the entropy’s generating function (i.e., h(t) = R SX̄F tX (x)dx) using a Caputo fractional-order derivative, we derive a generalized non-logarithmic fractional cumulative residual entropy (FCRE).
Slimane Benmahmoud
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A comparison between numerical solutions to fractional differential equations: Adams-type predictor-corrector and multi-step generalized differential transform method [PDF]
, 2017 In this note, two numerical methods of solving fractional differential equations (FDEs) are briefly described, namely predictor-corrector approach of Adams-Bashforth-Moulton type and multi-step generalized differential transform method (MSGDTM), and then
Ahrabi, Sima Sarv, Momenzadeh, Alireza
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About Edge Detection in Digital Images [PDF]
Radioengineering, 2018 Edge detection is one of the most commonly used procedures in digital image processing. In the last 30-40 years, many methods and algorithms for edge detection have been proposed.
M. Hagara, P. Kubinec
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Chaos in fractional order financial model with fractal–fractional derivatives
Partial Differential Equations in Applied Mathematics, 2023 Recently, a new differential operator which combines fractal differentiation and fractional differentiation with different kernels such as power law, exponential decay, and the Mittag–Leffler function has been introduced.
Krunal B. Kachhia
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