Field study of dispersion in a heterogeneous aquifer: 2. Spatial moments analysis, Water Resources Research, vol.22, issue.13, p.32933307, 1992. ,
DOI : 10.1029/92WR01757
On the concept of solution for fractional dierential equations with uncertainty, Nonlinear Analysis, p.28592862, 2010. ,
Time-delayed Perona-Malik type problems, Proceedings of the International Conference on Dierential Equations, pp.15-38, 2005. ,
Identication of moving pointwise sources in an advection-dispersion-reaction equation, Inverse Problems, vol.27, issue.22, p.pp, 2011. ,
Fractional-Order Anisotropic Diffusion for Image Denoising, IEEE Transactions on Image Processing, vol.16, issue.10, pp.2492-2502, 2007. ,
DOI : 10.1109/TIP.2007.904971
New Trends in Nanotechnology and Fractional Calculus Applications, pp.17-21, 2009. ,
DOI : 10.1007/978-90-481-3293-5
Determination of an unknown source parameter in two-dimensional heat equation, Applied Mathematics and Computation, vol.159, issue.3, pp.881-886, 2004. ,
DOI : 10.1016/j.amc.2003.08.082
Fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, issue.6, pp.844-856, 2002. ,
DOI : 10.1109/TPAMI.2002.1008390
Stable discretization of scalar and constrained vectorial Perona???Malik equation, Interfaces and Free Boundaries, vol.9, issue.4, pp.431-453, 2007. ,
DOI : 10.4171/IFB/172
A REGULARIZED PERONA-MALIK FUNCTIONAL: SOME ASPECTS OF THE GRADIENT DYNAMICS, EQUADIFF 2003, pp.22-26639, 2003. ,
DOI : 10.1142/9789812702067_0106
Collocation methods for Volterra integral and related functional equations, Cambridge Monographs Applied and Computational Mathematics, 2004. ,
DOI : 10.1017/CBO9780511543234
The staircasing effect in neighborhood filters and its solution, IEEE Transactions on Image Processing, vol.15, issue.6, pp.1499-1505, 2006. ,
DOI : 10.1109/TIP.2006.871137
URL : https://hal.archives-ouvertes.fr/hal-00271143
Runge???Kutta convolution quadrature methods for well-posed equations with memory, Numerische Mathematik, vol.43, issue.4, pp.614-55, 2007. ,
DOI : 10.1007/s00211-007-0107-9
Backward Euler method as a positivity preserving method for abstract integral equations of convolution type, Proceedings of Fractional Dierentiation and its Applications 06, pp.530-534, 2006. ,
Image Selective Smoothing and Edge Detection by Nonlinear Diffusion, SIAM Journal on Numerical Analysis, vol.29, issue.1, pp.182-193, 1992. ,
DOI : 10.1137/0729012
Uniqueness in an inverse problem for a one-dimensional fractional diusion equation, Inverse Problems, vol.25, issue.80, 2009. ,
A Galerkin procedure for the diusion subject to the specication of mass, SIAM J. Numer. Anal, vol.24, issue.3, p.499515, 1987. ,
Determination of a control parameter in a parabolic partial dierential equation, J. Austral. Math. Soc. Ser. B, vol.33, p.149163, 1991. ,
Some Advances on Image Processing by Means of Fractional Calculus, Nonlinear Science and Complexity, pp.265-271, 2011. ,
DOI : 10.1007/978-90-481-9884-9_31
Image processing by means of a linear integrodierential equation, IASTED, vol.34, pp.438-442, 2003. ,
Image structure preserving denoising using generalized fractional time integrals, Signal Processing, vol.92, issue.2, pp.553-563, 2012. ,
DOI : 10.1016/j.sigpro.2011.09.001
URL : https://hal.archives-ouvertes.fr/hal-00437341
On the Improvement of Volterra Equation Based Filtering for Image Denoising, Proceedings of IPCV 2011, pp.733-738 ,
URL : https://hal.archives-ouvertes.fr/hal-00589225
A Numerical Method for an Integro-Differential Equation with Memory in Banach Spaces: Qualitative Properties, SIAM Journal on Numerical Analysis, vol.41, issue.4, pp.1232-1241, 2003. ,
DOI : 10.1137/S0036142902402481
Color image denoising via sparse 3D collaborative ltering with grouping constraint in luminancechrominance space, IEEE International Conference on Image Processing, ICIP, 2007. ,
Denoising and Enhancement of Digital Images, Variational Methods, Integrodierential Equations, and Wavelets, 2008. ,
Regularity and Scale-Space Properties of Fractional High Order Linear Filtering, Lecture Notes in Computer Vision, vol.3459, pp.13-25, 2005. ,
DOI : 10.1007/11408031_2
Integrodifferential equations for continuous multiscale wavelet shrinkage, Inverse Problems and Imaging, vol.1, issue.1, pp.47-62, 2007. ,
DOI : 10.3934/ipi.2007.1.47
Cauchy problem for fractional diffusion equations, Journal of Differential Equations, vol.199, issue.2, pp.211-255, 2004. ,
DOI : 10.1016/j.jde.2003.12.002
Optimal Stopping Time Formulation of Adaptive Image Filtering, Applied Mathematics and Optimization, vol.43, issue.3, pp.245-258, 2001. ,
DOI : 10.1007/s00245-001-0006-x
The Parabolic Differential Equations and the Associated Semi-Groups of Transformations, The Annals of Mathematics, vol.55, issue.3, pp.468-519, 1952. ,
DOI : 10.2307/1969644
Diusion processes in one dimension, Trans. Amer. Math. Soc, 77, issue.1, pp.1-33, 1952. ,
Integro-dierential equation which interpolates the heat equation and the wave equation, Osaka Journal of Mathematics, vol.20, pp.27-319, 1990. ,
Integro-dierential equation which interpolates the heat equation and the wave equation (ii), Osaka Journal of Mathematics, vol.27, issue.20, pp.797-804, 1990. ,
Necessary conditions for the existence of global solutions to systems of fractional dierential equations, Fractional Calculus & Applied Analysis, vol.11, issue.22, pp.281298-281337, 2008. ,
Analysis of a system of nonautonomous fractional dierential equations involving Caputo derivatives, J. Math. Anal. Appl, vol.328, p.10261033, 2007. ,
Positive solutions of a system of non-autonomous fractional dierential equations, J. Math. Anal. Appl, vol.302, p.5664, 2005. ,
Fractional Calculus: integral and dierential equations of fractional order, Fractals and Fractional Calculus in Continuum Mechanics, pp.223276-223316, 1997. ,
Nonlinear anisotropic filtering of MRI data, IEEE Transactions on Medical Imaging, vol.11, issue.2, pp.221-232, 1992. ,
DOI : 10.1109/42.141646
Strange attractors in delayed cellular neural networks, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.40, issue.11, pp.849-853, 1993. ,
DOI : 10.1109/81.251826
A new well-posed nonlinear nonlocal diusion, Nonlinear Analysis: TMA(2010) ,
A new nonlocal nonlinear diffusion of image processing, Journal of Differential Equations, vol.246, issue.12, pp.4731-4742, 2009. ,
DOI : 10.1016/j.jde.2009.03.017
Two Enhanced Fourth Order Diffusion Models for Image Denoising, Journal of Mathematical Imaging and Vision, vol.5, issue.11, pp.188-198, 2011. ,
DOI : 10.1007/s10851-010-0256-9
Two New Nonlinear Nonlocal Diffusions for Noise Reduction, Journal of Mathematical Imaging and Vision, vol.9, issue.1, pp.25-37, 2009. ,
DOI : 10.1007/s10851-008-0108-z
Uning probabilistic and variational estimation, IEEE Signal Processing Magazine, vol.2, pp.37-47, 2002. ,
DOI : 10.1109/msp.2002.1028351
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.4387
Dispersive transport of ions in column experiments: An explanation of long-tailed profiles, Water Resources Research, vol.10, issue.5, p.10271033, 1998. ,
DOI : 10.1029/98WR00214
Applications of Fractional Caluclus in Physics, World Scientic, 2000. ,
Theory of pattern recognition, Electronics and Communications, p.134, 1963. ,
The two-dimensional heat equation with nonlocal boundary conditions, Differential Equations, vol.34, issue.5, pp.982987-982999, 2000. ,
DOI : 10.1007/BF02754498
MODELING THE CARDIAC TISSUE ELECTRODE INTERFACE USING FRACTIONAL CALCULUS, IFAC Proceedings Volumes, vol.39, issue.11, pp.1431-1442, 2008. ,
DOI : 10.3182/20060719-3-PT-4902.00056
The random walk's guide to anomalous diffusion: a fractional dynamics approach, Physics Reports, vol.339, issue.1, pp.1-77, 2000. ,
DOI : 10.1016/S0370-1573(00)00070-3
A Two-Point Boundary Value Problem for a Heat Conduction Equation, Dierentsialnye Uravneniya, vol.15, issue.7, pp.1284-1295, 1979. ,
Inverse parabolic problems with the final overdetermination, Communications on Pure and Applied Mathematics, vol.42, issue.2, pp.185-209, 1991. ,
DOI : 10.1002/cpa.3160440203
Laplace's transform of fractional order via the MittagLeer function and modied RiemannLiouville derivative, Appl. Math. Lett, vol.22, p.16591664, 2009. ,
Problems of determining the temperature and density of heat sources from the initial and final temperatures, Journal of Applied and Industrial Mathematics, vol.4, issue.3, pp.332-339, 2010. ,
DOI : 10.1134/S199047891003004X
Solution of nonlinear diffusion appearing in image smoothing and edge detection, Applied Numerical Mathematics, vol.17, issue.1, pp.47-59, 1995. ,
DOI : 10.1016/0168-9274(95)00008-I
Slow and fast diusion eects in image processing, Computing and Visualization in Science, pp.185-195, 2001. ,
On the inverse problem of determining the right-hand side of a parabolic equation under an integral overdetermination condition, Mathematical Notes, vol.73, issue.2, p.482493, 2005. ,
DOI : 10.1007/s11006-005-0047-6
ON THE COMPLETENESS OF THE EIGENFUNCTIONS OF SOME CLASSES OF NON-SELFADJOINT LINEAR OPERATORS, Russian Mathematical Surveys, vol.26, issue.4, p.60, 1971. ,
DOI : 10.1070/RM1971v026n04ABEH003985
The persona-malik paradox, SIAM J. Appl. Math, vol.147, issue.125, pp.13281342-13281375, 1997. ,
Theory and Applications of Fractional Dierential Equations, pp.17-63, 2006. ,
Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives, Journal of Mathematical Analysis and Applications, vol.312, issue.2, pp.312-488501, 2005. ,
DOI : 10.1016/j.jmaa.2005.03.054
The prole of blowing-up solutions to a nonlinear system of fractional dierential equations, Nonlinear Analysis, pp.3723-3736, 2010. ,
Determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time, Applied Mathematics and Computation, vol.218, issue.1, pp.163170-60 ,
DOI : 10.1016/j.amc.2011.05.084
URL : https://hal.archives-ouvertes.fr/hal-00549130
Determination of an unknown source term for a one dimensional fractional diusion equation with an integral type overdetermination condition ,
Sequential fractional dierential equations with Hadamard derivative, Commun. Nonlinear Sci. Numer. Simul, vol.16, issue.12, p.46894697, 2011. ,
Integral equations and initial value problems for nonlinear differential equations of fractional order, Nonlinear Analysis, pp.2529-2569, 2009. ,
Source identification for the heat equation, Applied Mathematics Letters, vol.1, issue.3, pp.241-245, 1988. ,
DOI : 10.1016/0893-9659(88)90084-5
Theory of Fractional Dynamic Systems, p.40, 2009. ,
Fractional cable equation for anomalous electrodiusion in nerve cells: innite domain solutions, J. Math. Biol, vol.59, pp.761808-761847, 2009. ,
Digital image smoothing and the sigma lter, Computer Vision, Graphics, and Image Processing, pp.253-269, 1983. ,
Adaptive, Fast, and Oblivious Convolution in Evolution Equations with Memory, SIAM Journal on Scientific Computing, vol.30, issue.2, pp.1015-1037, 2008. ,
DOI : 10.1137/060674168
On the numerical inversion of the Laplace transform of certain holomorphic mappings, Applied Numerical Mathematics, vol.51, issue.2-3, pp.289-303, 2004. ,
DOI : 10.1016/j.apnum.2004.06.015
Convolution quadrature and discretized operational calculus I, Numerische Mathematik, pp.129-145, 1988. ,
Convolution quadrature and discretized operational calculus. II, Numerische Mathematik, vol.23, issue.4, pp.413-425, 1988. ,
DOI : 10.1007/BF01462237
URL : http://www.digizeitschriften.de/download/PPN362160546_0052/PPN362160546_0052___log13.pdf
Convolution Quadrature Revisited, BIT Numerical Mathematics, vol.44, issue.3, pp.126-128, 2004. ,
DOI : 10.1023/B:BITN.0000046813.23911.2d
Runge-Kutta methods for parabolic equations and convolution quadrature, Mathematics of Computation, vol.60, issue.201, pp.105-131, 1993. ,
DOI : 10.1090/S0025-5718-1993-1153166-7
Estimation of parameters in fractional subdiffusion equations by the time integral characteristics method, Computers & Mathematics with Applications, vol.62, issue.3, pp.834-844, 2011. ,
DOI : 10.1016/j.camwa.2011.03.058
Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time, IEEE Transactions on Image Processing, vol.12, issue.12, pp.1579-1590, 2003. ,
DOI : 10.1109/TIP.2003.819229
Recent history of fractional calculus, Communications in Nonlinear Science and Numerical Simulation, vol.16, issue.3, pp.1140-1153, 2011. ,
DOI : 10.1016/j.cnsns.2010.05.027
Fractional calculus and continuous-time finance II: the waiting-time distribution, Physica A: Statistical Mechanics and its Applications, vol.287, issue.3-4, pp.468-481, 2000. ,
DOI : 10.1016/S0378-4371(00)00386-1
Fractional calculus and waves in linear viscoelaticity, p.17, 2010. ,
Fractional differentiation for edge detection, Signal Processing, vol.83, issue.11, pp.2421-2432, 2003. ,
DOI : 10.1016/S0165-1684(03)00194-4
Derivatives of noninteger order and their applications, Dissertations Mathematicae, CCCXXVIII, 1993. ,
The Solution of a Nonlocal Boundary Value Problem by the Spectral Method, Dierential Equations, vol.35, issue.8, pp.1105-1112, 1999. ,
Selection of Optimal Stopping Time for Nonlinear Diusion Filtering, Int. journal of Computer Vision, vol.52, pp.189203-189216, 2003. ,
Fractional variational calculus with classical and combined Caputo derivatives, Nonlinear Analysis, TMA, vol.75, p.15071515, 2012. ,
Coupled Volterra Equations with Blow-Up Solutions, Journal of Integral Equations and Applications, vol.7, issue.4, pp.516-51, 1995. ,
DOI : 10.1216/jiea/1181075901
Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.12, issue.7, pp.629-639, 1990. ,
DOI : 10.1109/34.56205
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.108.2553
Fractional-Order Nonlinear Systems Modelling, Analysis and Simulations, 2011. ,
Transmission of dengue hemorrhagic fever in an age structured population, Mathematical and Computer Modelling, vol.37, issue.9-10, pp.949-961, 2003. ,
DOI : 10.1016/S0895-7177(03)00111-0
Fractional Derivatives in Dengue Epidemics, AIP Conf. Proc. 1389, pp.739-74210 ,
DOI : 10.1063/1.3636838
Relaxation time distribution for an anomalously diusing particle, Physica A, vol.390, p.28632879, 2011. ,
A singular intgeral equation with a generalized Mittag-Leer function in the kernel, Yokohama Math. J, vol.19, issue.82, pp.7-15, 1971. ,
Evolutionary Integral Equations and Applications, 1993. ,
Certain inverse problems for parabolic equations, Journal of Mathematical Sciences, vol.54, issue.2, pp.2422-2433, 2008. ,
DOI : 10.1007/s10958-008-0140-y
Improving satellite image classification by using fractional type convolution filtering, International Journal of Applied Earth Observation and Geoinformation, vol.12, issue.4, pp.298-301, 2010. ,
DOI : 10.1016/j.jag.2010.02.008
Nonlinear total variation based noise removal algorithm, PhysicaD, pp.60-259, 1992. ,
DOI : 10.1016/0167-2789(92)90242-f
Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, 2007. ,
DOI : 10.1007/978-1-4020-6042-7
URL : https://hal.archives-ouvertes.fr/hal-00401720
Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, pp.17-63, 1993. ,
Fractional calculus and continuous-time finance, Physica A: Statistical Mechanics and its Applications, vol.284, issue.1-4, pp.376-384, 2000. ,
DOI : 10.1016/S0378-4371(00)00255-7
URL : http://arxiv.org/abs/cond-mat/0001120
A stability estimate of an inverse problem in nancial prospection, Appl. Math. Comput, vol.150, pp.803-810, 2004. ,
Nonclassical boundary-value problems. I, Journal of Mathematical Sciences, vol.28, issue.1, pp.199-327, 2008. ,
DOI : 10.1007/s10958-008-9218-9
On an inequality arising in fractional oscillator theory, Fractional Calculus & Applied Analysis, vol.7, p.1120, 2004. ,
Fractional Dynamics Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, 2010. ,
A blow up result for a fractionally damped wave equation NoDEA, p.215226, 2005. ,
Bilateral ltering for grey and color images, Proceedings of the 6th International Conference on Computer Vision, pp.839-846, 1998. ,
On boundary conditions for multidimensional diusion processes , Theory of probability and its applications, pp.164-177, 1959. ,
Estimating the gradient threshold in the perona-malik equation, IEEE Signal Processing Magazine, vol.23, issue.3, pp.39-46, 2004. ,
DOI : 10.1109/MSP.2004.1296541
A semidicrete nonlinear scale-space theory and its relation to the Perona-Malik paradox, Advances in Computer Vision, pp.1-10, 1997. ,
Anisotropic Diusion in Image Processing, Teubner, pp.125-127, 1998. ,
An inverse problem for fractional diffusion equation in 2-dimensional case: Stability analysis and regularization, Journal of Mathematical Analysis and Applications, vol.393, issue.1, 2012. ,
DOI : 10.1016/j.jmaa.2012.03.013
A new regularization method for solving a time-fractional inverse diffusion problem, Journal of Mathematical Analysis and Applications, vol.378, issue.2, pp.418-431, 2011. ,
DOI : 10.1016/j.jmaa.2011.01.067
Inverse source problem for a fractional diusion equation, Inverse Problems, vol.27273, issue.80, 2011. ,