Rudolf Gorenflo

Q: What Schools Are Affiliated With Rudolf Gorenflo

Rudolf Gorenflo is affiliated with the following schools: University of Bonn, University of Duisburg-Essen, Karlsruhe Institute of Technology, University of Tokyo, Free University of Berlin

Rudolf Gorenflo's AcademicInfluence.com Rankings

Rudolf Gorenflo

Mathematics

#5670

World Rank

#7970

Historical Rank

Measure Theory

#2163

World Rank

#2607

Historical Rank

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Mathematics

Rudolf Gorenflo's Degrees

PhD Mathematics University of Bonn

Why Is Rudolf Gorenflo Influential?

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According to Wikipedia, Rudolf Gorenflo was a German mathematician. Biography Gorenflo was born on July 31, 1930, in Friedrichstal, Germany. From 1950 to 1956 he attended Karlsruhe Institute of Technology from which he received his diploma in mathematics. From 1957 to 1961 he became a scientific assistant there and for a year later worked at Standard Electric Lorenz Company. From 1962 to 1970 he worked at the Max Planck Institute for Plasma Physics, at Garching not too far away from Munich. He was a resident in mathematics at the Technical University in Aachen in 1970 and a year later became a professor there.

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Rudolf Gorenflo's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Fractional Calculus: Integral and Differential Equations of Fractional Order (2008) (1449)
Mittag-Leffler Functions, Related Topics and Applications (2014) (871)
Fractional calculus and continuous-time finance (2000) (784)
Multi-index Mittag-Leffler Functions (2014) (740)
On Mittag-Leffler-type functions in fractional evolution processes (2000) (537)
Fractional calculus and continuous-time finance II: the waiting-time distribution (2000) (495)
AN OPERATIONAL METHOD FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS WITH THE CAPUTO DERIVATIVES (1999) (441)
Time Fractional Diffusion: A Discrete Random Walk Approach (2002) (363)
Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations. (2002) (357)
Discrete random walk models for space-time fractional diffusion (2002) (288)
Abel Integral Equations: Analysis and Applications (1991) (284)
Fractional Calculus and Continuous-Time Finance III : the Diffusion Limit (2001) (276)
Analytical properties and applications of the Wright function (2007) (264)
Wright functions as scale-invariant solutions of the diffusion-wave equation (2000) (260)
Fractional diffusion in inhomogeneous media (2005) (231)
Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation. (2004) (197)
Time-fractional derivatives in relaxation processes: a tutorial survey (2008) (197)
Hilfer-Prabhakar derivatives and some applications (2014) (194)
A fractional generalization of the Poisson processes (2007) (190)
Time-fractional Diffusion of Distributed Order (2007) (185)
Some aspects of fractional diffusion equations of single and distributed order (2007) (173)
Time-fractional diffusion equation in the fractional Sobolev spaces (2015) (172)
Probability distributions generated by fractional diffusion equations (2007) (159)
Continuous-time random walk and parametric subordination in fractional diffusion (2007) (157)
Fractional calculus and stable probability distributions (1998) (132)
Some recent advances in theory and simulation of fractional diffusion processes (2007) (132)
Abel Integral Equations (1990) (131)
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density (2013) (130)
Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk (2007) (126)
On the generalized mittag-leffler type functions (1998) (113)
The Two Forms of Fractional Relaxation of Distributed Order (2007) (113)
Probability distributions generated by fractional diffusion equations 1 (2007) (111)
Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights. (2008) (102)
Anomalous waiting times in high-frequency financial data (2003) (90)
Approximation of Levy-Feller Diffusion by Random Walk (1999) (89)
Fractional diffusion: probability distributions and random walk models (2002) (87)
On autoconvolution and regularization (1994) (84)
Cauchy and Nonlocal Multi-Point Problems for Distributed Order Pseudo-Differential Equations, Part One (2005) (77)
Random walk models approximating symmetric space-fractional diffusion processes (2012) (76)
Mellin transform and subordination laws in fractional diffusion processes (2007) (75)
Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction (2002) (73)
Discrete random walk models for symmetric Lévy–Feller diffusion processes (1999) (72)
FRACTIONAL CALCULUS : Some Numerical Methods (2001) (66)
Beyond the Poisson renewal process: A tutorial survey (2007) (65)
Fractional Oscillations And Mittag-Leffler Functions (1996) (64)
Continuous time random walk, Mittag-Leffler waiting time and fractional diffusion: mathematical aspects (2007) (61)
Renewal processes of Mittag-Leffler and Wright type (2007) (58)
Simply and multiply scaled diffusion limits for continuous time random walks (2005) (50)
Operator theoretic treatment of linear Abel integral equations of first kind (1999) (50)
Discrete and Continuous Random Walk Models for Space-Time Fractional Diffusion (2004) (50)
REVISITING THE DERIVATION OF THE FRACTIONAL DIFFUSION EQUATION (2002) (48)
Sub-diffusion equations of fractional order and their fundamental solutions (2007) (45)
Fully discrete random walks for space-time fractional diffusion equations (2003) (45)
Convergence of the Grünwald-Letnikov scheme for time-fractional diffusion (2007) (44)
Operationl method for solving generalized abel integral equation of second kind (1997) (37)
A noncharacteristic cauchy problem for the heat equation (1991) (36)
From Power Laws to Fractional Diffusion: the Direct Way (2007) (32)
Parametric subordination in fractional diffusion processes (2012) (31)
Abel integral equations with special emphasis on applications (1996) (30)
Nonlinear two-term time fractional diffusion-wave problem (2010) (29)
Parametric subordination in fractional diffusion processes 1 (2012) (29)
On the Fractional Poisson Process and the Discretized Stable Subordinator (2013) (28)
Mittag-Leffler Waiting Time, Power Laws,Rarefaction, Continuous Time Random Walk, Diffusion Limit (2010) (27)
Towards the Cauchy problem for the Laplace equation (1992) (25)
The Classical Mittag-Leffler Function (2020) (25)
Mittag-Leffler function: properties and applications (2019) (24)
Speculative option valuation and the fractional diffusion equation (2005) (23)
Funktionentheoretische Bestimmung des Aussenfeldes zu einer zweidimensionalen magnetohydrostatischen Konfiguration (1965) (22)
Asymptotics of singular values of fractional integral operators (1994) (21)
FRACTIONAL RELAXATION OF DISTRIBUTED ORDER (2006) (21)
Discrete and Continuous Random Walk Models for Space-Time Fractional Diffusion (2006) (20)
Simulation of the continuous time random walk of the space-fractional diffusion equations (2008) (19)
Laplace-Laplace analysis of the fractional Poisson process (2013) (19)
Solution of an Abel-type integral equation in the presence of noise by quadratic programming (1966) (18)
On Optimal Regularization Methods for Fractional Differentiation (1999) (16)
A Multi-Dimensional Hausdorff Moment Problem: Regularization by Finite Moments (1999) (16)
Asymptotics of singular values of Volterra integral operators (1996) (15)
ON SOLVABILITY OF LINEAR FRACTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES∗ (2005) (15)
On the Intertrade Waiting-time Distribution (2005) (15)
Fractional Diffusion in Finance : Basic Theory (2001) (15)
COMPUTATION OF ROUGH SOLUTIONS OF ABEL INTEGRAL EQUATIONS (1987) (14)
FRACTIONAL RELAXATION AND TIME-FRACTIONAL DIFFUSION OF DISTRIBUTED ORDER (2006) (13)
Singular value decomposition of fractional integration operators in L2-spaces with weights (1995) (11)
On the cauchy problems for systems of partial differential equations with a distinguished variable (1991) (11)
Locally controllable regularization of fractional derivatives (1994) (11)
Differenzenschemata monotoner Art fuer lineare parabolische Randwertaufgaben (1971) (10)
On the regularization of fractional differentiation of arbitrary positive order (1994) (10)
Conservative Difference Schemes for Diffusion Problems (1978) (9)
CONTINUOUS TIME RANDOM WALK AND TIME FRACTIONAL DIFFUSION: A NUMERICAL COMPARISON BETWEEN THE FUNDAMENTAL SOLUTIONS (2005) (9)
Über S. Gerschgorins Methode der Fehlerabschatzung bei Differenzenverfahren (1973) (8)
Fractional relaxation-oscillation phenomena (2019) (8)
Theory and Practice of Geophysical Data Inversion (1992) (8)
Geophysical Data Inversion Methods and Applications (1990) (8)
Design of a neutron scattering chamber using Monte Carlo calculations (1969) (8)
On the dependence of asymptotics of s-numbers of fractional integration operators on weight functions (1997) (7)
The Mittag-Leffler function in the thinning theory for renewal processes (2018) (7)
Power laws, random walks, and fractional diffusion processes as well scaled refinement limits (2005) (7)
Locally controllable regularization of Abel integral equations via operator complementation (1997) (7)
The Tomato Salad Problem In Spherical Stereology (1996) (6)
The Grünwald-Letnikov Difference Operator and Regularization of the Weyl Fractional Differentiation (1994) (6)
Nichtnegativitäts-und substanzerhaltende Differenzenschemata für lineare Diffusionsgleichungen (1970) (6)
STOCHASTIC PROCESSES RELATED TO THE TIME-FRACTIONAL DIFFUSION-WAVE EQUATION (2015) (5)
A renewal process of Mittag-Leffler type (2004) (5)
Conservative difference schemes for diffusion problems with boundary and interface conditions (1980) (5)
Regularization of a generalized Abel integral equation (1992) (5)
Operator theoretic approach to the Caputo derivative and the fractional diffusion equations (2014) (5)
Limitations of the permeability-limited compartment model in estimating vascular permeability and interstitial volume fraction in DCE-MRI. (2011) (4)
Probability Density (2020) (4)
Monotonic Difference Schemes for Weakly Coupled Systems of Parabolic Differential Equations (1969) (4)
Loesung einer Abelschen Integralgleichung bei Anwesenheit von Stoerungen mittels quadratischer Optimierung (1965) (4)
Approximation of Discrete Probability Distributions in Spherical Stereology (1986) (4)
The waiting-time distribution of LIFFE bond futures (2000) (4)
The Two-Parametric Mittag-Leffler Function (2020) (3)
Berechnung des ebenen Magnetfeldes paralleler Leiter endlicher Dicke mittels komplexer Analysis (1967) (3)
Applications to Fractional Order Equations (2020) (3)
Sobolev-Orlici spaces of infinite order and nonlinear differential equations (1990) (3)
Differenzenschemata vom Irrfahrttypus fuer die Differentialgleichung von Fokker-Planck-Kolmogorov (1969) (3)
A nonlinear Abel integral equation (1991) (3)
Monte Carlo Simulation of a Knudsen Gas Flow with Due Allowance for the Sojourn Time (1967) (3)
Newtonsche Aufheizung, Abelsche Integralgleichungen zweiter Art und Mittag-Leffler-Funktionen (1987) (2)
Monotonic difference schemes for weakly coupled parabolic systems (1969) (2)
Eine Anwendung der Funktionentheorie in der Magnetohydrostatik (1964) (2)
Applications of a transformed abel integral equation (1991) (2)
Regularization of a nonlinear integral equation of gravimetry (1997) (2)
Über das Il’in — Differenzenschema für die Diffusions — Konvektions — Gleichung (1982) (2)
Applications to Stochastic Models (2020) (2)
On nondegenerate and degenerate nonlinear Abel integral equations of the first kind (1994) (2)
Beyond the Poisson renewal process (2007) (2)
Non-Boltzmann Equilibrium Probability Densities for Non-Linear L\'{e}vy Oscillator (2000) (2)
Singular value decomposition of fractional integration operators in L 2 – spaces with weights (2005) (2)
SUBORDINATION IN FRACTIONAL DIFFUSION PROCESSES VIA CONTINUOUS TIME RANDOM WALK (2009) (2)
Applications to Deterministic Models (2020) (2)
A uniqueness theorem for a nonlinear integral equation of gravimetry (1996) (2)
Monoton einschliessende Iterationsverfahren for invers-isotone Diskretisierung nicht-linearer Zwei-Punkt-Randwertaufgaben zweiter Ordnung (1974) (2)
Über ganze transzendente Funktionen von regelmäßigem Wachstum (1962) (1)
Mittag-Leffler Functions with Three Parameters (2020) (1)
International Centre for Mechanical Sciences Palazzo del Torso, Piazza Garibaldi, Udine, Italy FRACTIONAL CALCULUS : Integral and Differential Equations of Fractional Order (2008) (1)
Differenzenschemata monotoner Art für lineare parabolische Randwertaufgaben.- Difference schemes of monotonic type for linear parabolic boundary value problems. (1970) (1)
All Ill-posed problem for the heat equation (1991) (1)
Historical Overview of the Mittag-Leffler Functions (2020) (1)
Survival probability of LIFFE bond futures via the Mittag-Leffler function (2002) (1)
Analysis of parabolic difference schemes by Gerschgorin's method (1983) (1)
On Sobolev-Orlicz spaces of infinite order for a full Euclidean space1 (1991) (1)
Fe b 20 02 RETARDING SUB-AND ACCELERATING SUPER-DIFFUSION GOVERNED BY DISTRIBUTED ORDER FRACTIONAL DIFFUSION EQUATIONS (2008) (1)
On difference schemes for parabolic differential equations with derivative boundary conditions (1971) (1)
Calculation of the Current Flow Directions in a Channel with Staggered Electrodes Under MHD Generator Conditions (1970) (1)
Model optimization in exploration geophysics 2 : proceedings of the 5th International Mathematical Geophysics Seminar held at the Free University of Berlin, Feb. 4-7, 1987 (1988) (1)
A Fractional Generalization of the Poisson Processes and Some of its Properties (2013) (1)
Berechnung des zweidimensionalen Magnetfeldes einer geraden Anzahl von Ioffe-Stäben mittels komplexer Analysis (1965) (1)
Über die singulären Stellen der Lösungen nichtlinearer Differentialgleichungen (1961) (1)
Behandlung ebener magnetohydrostatischer Gleichgewichtsprobleme mittels komplexer Analysis. (1972) (1)
Diskrete Diffusionsmodelle und monotone Differenzenschemata fuer parabolische Differentialgleichungen (1969) (1)
Numerische Simulation von Diffusionsprozessen mit nichtnegativitätserhaltenden konservativen Differenzenverfahren / Numerical Simulation of Diffusion Processes with conservative difference schemes of non-negative type (1982) (1)
Numerische Simulation von Diffusionsprozessen mit nichtnegativitätserhaltenden konservativen Differenzenverfahren / (1982) (1)
6. Regularization of some inverse problems in potential theory (2002) (0)
Monte Carlo Simulation of the Flow of a Knudsen Gas With Due Allowance for the Sojourn Time; MONTE-CARLO-SIMULATION DER STROEMUNG EINES KNUDSEN-GASES UNTER BERUECKSICHTIGUNG DER VERWEILZEIT (1965) (0)
Relations between abel transform and other integral transforms (1991) (0)
7. Regularization of some inverse problems in heat conduction (2002) (0)
Zweidimensionale innenfeldfreie Plasmakonfigurationen im Gleichgewicht mit einem äußeren Magnetfeld (1964) (0)
Diffusion‐wave phenomena (2007) (0)
Inverse modeling in exploration geophysics : proceedings of the 6th International Mathematical Geophysics Seminar held at the Free University of Berlin, Feb. 3-6, 1988 (1989) (0)
Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density (2013) (0)
1. Mathematical preliminaries (2002) (0)
Inversion from redundant data (1993) (0)
[On pseudo-random generators and their statistical properties]. (1965) (0)
Applied Nonlinear Functionalanalysis: Variational Methods and Ill-Posed Problems (1982) (0)
Approximating the Solution to the Cauchy Problem and the Boundary Value for the Laplace Equation (1992) (0)
Nonlinear abel integral equations of second kind (1991) (0)
Applications of Abel's original integral equation: Determination of potentials (1991) (0)
Fractional diffusion and parametric subordination (2019) (0)
Monte-Carlo-Simulation der Strömung eines KNUDSEN-Gases unter Berücksichtigung der Verweilzeit. - Monte Carlo Simulation of the Flow of KNUDSEN Gas with Due Allowance for the Sojourn Time (1965) (0)
D ec 2 00 0 NON-BOLTZMANN EQUILIBRIUM PROBABILITY DENSITIES FOR NON-LINEAR LÉVY OSCILLATOR (2008) (0)
Prüss, J., Evolutionary Integral Equations and Applications. Basel etc., Birkhäuser Verlag 1993, XXVI, 366 pp., sfr 168 ISBN 3-7643-2876-2 (Monographs in Mathematics 87) (1995) (0)
On numerical treatment of first kind abel integral equations (1991) (0)
SUPER-DIFFUSION GOVERNED BY DISTRIBUTED ORDER FRACTIONAL DIFFUSION EQUATIONS (2018) (0)
Mikhlin,S. G.; Morozov, N. F.; Paukshto, M. V.: The Integral Equations of the Theory of Elasticity. Stuttgart/Leipzig, B. G. Teubner Verlagsgesellschaft 1995. 375 S., 19 Abb., DM 64,80. ISBN 3‐8154‐2060‐1 (Teubner‐Texte zur Mathematik 135) (1996) (0)
The Classical Wright Function (2020) (0)
Maz'ya, V. G.; Nikol‐skii, S. M. (eds.), Analysis. IV. Berlin etc., Springer‐Verlag 1991. VII, 233 pp., DM 128,00. ISBN 3–540–51997‐1 (Encyclopaedia of Mathematical Sciences 27) (1993) (0)
Monotone Differenzenschemata für parabolische Differentialgleichungen mit nichtlinearen Randbedingungen (1970) (0)
Ebene magnetohydrostatische Gleichgewichte mit Innenfeld (1967) (0)
Calculation of the Two-Dimensional Magnetic Field of an Even Number of Ioffe Bars by Complex Analysis; BERECHNUNG DES ZWEIDIMENSIONALEN MAGNETFELDES EINER GERADEN ANZAHL VON IOFFE-STAEBEN MITTELS KOMPLEXER ANALYSIS (1965) (0)
5. Analytic functions: reconstruction and Sinc approximations (2002) (0)
Multi-index and Multi-variable Mittag-Leffler Functions (2020) (0)
Einige Testmethoden für Zufallsgeneratoren (1966) (0)
The Tomato Salad Problem In Spherical Stereology R. Gorenflo (2002) (0)
Sakhnovich, L. A.: Integral Equations with Difference Kernels on Finite Intervals. Basel etc., Birkhäuser 1996. VI, 177 pp., sFr 98.00/DM 118,00. ISBN 3‐7643‐5267‐1 (OT 84) (1997) (0)
Numerische Methoden zur Lösung einer ABELschen Integralgleichung (1964) (0)
Plane Magnetohydrostatic Equilibria with Interior Field; EBENE MAGNETOHYDROSTATISCHE GLEICHGEWICHTE MIT INNENFELD (1965) (0)
Differenzenschemata monotoner Art für schwach gekoppelte Systeme parabolischer Differentialgleichungen mit gemischten Randbedingungen (1971) (0)
Wolfersdorf, L. V., Inverse und schlecht gestellte Probleme. Eine Einführung. Berlin, Akademie Verlag 1994. 32 S., DM 18.–. ISBN 3‐05‐501649‐1 (Sitzungsberichte der Sächsischen Akademie der Wissenschaften zu Leipzig. Math.‐naturwiss. Klasse, Bd. 124, Heft 5) (1995) (0)
Explicit Viscosity Solutions for @u=@t + H(t; U; R X U) = 0 (1997) (0)
THE FUNDAMENTAL SOLUTION OF THE DISTRIBUTED ORDER FRACTIONAL WAVE EQUATION IN ONE SPACE DIMENSION IS A PROBABILITY DENSITY (2013) (0)
Probability Distributions and Continuous Time Random Walk 1 (2007) (0)
Fractional differentiation of the product of Bessel functions of the first kind (2016) (0)
Über die Zentralindices der Ableitungen einer ganzen transzendenten Funktion (1961) (0)
Illposedness and stabilization of linear abel integral equations of first kind (1991) (0)
Basic theory and representation formulas (1991) (0)
Funktionentheoretische Bestimmung der Dichte elektrischer Stroeme, die ein in einem Gebiet vorgegebenes Magnetfeld erzeugen (1967) (0)
Smoothing properties of the abel operators (1991) (0)
Introduction (2020) (0)
Existence and Uniqueness Theorems (2021) (0)
On Explicit Viscosity Solutions for @u=@t + H(u; R X U) = 0 (1997) (0)
Determination of Shape and Mass Density fromGravity Anomaly Measurements : Some Uniqueness Results (1997) (0)
2. Regularization of moment problems by truncated expansion and by the Tikhonov method (2002) (0)
3. Backus-Gilbert regularization of a moment problem (2002) (0)
FRACTIONAL CALCULUS AND SPECIAL FUNCTIONS 1 FRACTIONAL CALCULUS AND SPECIAL FUNCTIONS (2008) (0)
Time series models associated with Mittag-Leffler type distributions and its properties (2016) (0)
4. The Hausdorff moment problem: regularization and error estimates (2002) (0)

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