Guy Jumarie

Guy Jumarie's AcademicInfluence.com Rankings

Guy Jumarie

Mathematics

#7497

World Rank

#10185

Historical Rank

Applied Mathematics

#346

World Rank

#373

Historical Rank

Measure Theory

#2224

World Rank

#2673

Historical Rank

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Mathematics

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Guy Jumarie'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

Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results (2006) (956)
Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions (2009) (459)
Derivation and solutions of some fractional Black-Scholes equations in coarse-grained space and time. Application to Merton's optimal portfolio (2010) (225)
On the representation of fractional Brownian motion as an integral with respect to (dt)alpha (2005) (182)
Laplace's transform of fractional order via the Mittag-Leffler function and modified Riemann-Liouville derivative (2009) (162)
Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution (2007) (144)
New stochastic fractional models for Malthusian growth, the Poissonian birth process and optimal management of populations (2006) (119)
Cauchy's integral formula via the modified Riemann-Liouville derivative for analytic functions of fractional order (2010) (111)
Stochastic differential equations with fractional Brownian motion input (1993) (102)
On the solution of the stochastic differential equation of exponential growth driven by fractional Brownian motion (2005) (100)
Lagrangian mechanics of fractional order, Hamilton–Jacobi fractional PDE and Taylor’s series of nondifferentiable functions (2007) (88)
Stock exchange fractional dynamics defined as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional Black-Scholes equations (2008) (87)
Fractional master equation: non-standard analysis and Liouville–Riemann derivative (2001) (80)
Maximum Entropy, Information Without Probability and Complex Fractals: Classical and Quantum Approach (2000) (77)
An approach via fractional analysis to non-linearity induced by coarse-graining in space (2010) (74)
On the derivative chain-rules in fractional calculus via fractional difference and their application to systems modelling (2013) (69)
Probability calculus of fractional order and fractional Taylor's series application to Fokker-Planck equation and information of non-random functions (2009) (58)
Fractional Hamilton-Jacobi equation for the optimal control of nonrandom fractional dynamics with fractional cost function (2007) (55)
A Fokker-Planck equation of fractional order with respect to time (1992) (52)
Relative Information — What For? (1990) (51)
Fractional Brownian motions via random walk in the complex plane and via fractional derivative. Comparison and further results on their Fokker–Planck equations (2004) (49)
An approach to differential geometry of fractional order via modified Riemann-Liouville derivative (2012) (45)
Relative Information: Theories and Applications (2011) (43)
Lagrange characteristic method for solving a class of nonlinear partial differential equations of fractional order (2006) (39)
Modeling fractional stochastic systems as non-random fractional dynamics driven by Brownian motions (2008) (37)
The Minkowski's space-time is consistent with differential geometry of fractional order (2007) (36)
From Lagrangian mechanics fractal in space to space fractal Schrödinger’s equation via fractional Taylor’s series (2009) (34)
FOURIER'S TRANSFORM OF FRACTIONAL ORDER VIA MITTAG-LEFFLER FUNCTION AND MODIFIED RIEMANN-LIOUVILLE DERIVATIVE (2008) (30)
Merton's model of optimal portfolio in a Black-Scholes Market driven by a fractional Brownian motion with short-range dependence (2005) (26)
SCHRÖDINGER EQUATION FOR QUANTUM FRACTAL SPACE–TIME OF ORDER n VIA THE COMPLEX-VALUED FRACTIONAL BROWNIAN MOTION (2001) (25)
Further advances on the general thermodynamics of open systems via information theory: effective entropy, negative information (1975) (22)
A PRACTICAL VARIATIONAL APPROACH TO STOCHASTIC OPTIMAL CONTROL VIA STATE MOMENT EQUATIONS (1995) (21)
New results on Fokker–Planck equations of fractional order (2001) (20)
Further results on the information theory of deterministic functions and its application to pattern recognition (1990) (19)
On the fractional solution of the equation f(x + y) = f(x)f(y) and its application to fractional Laplace's transform (2012) (18)
Possibility‐Probability Transformation: A New Result via Information Theory of Deterministic Functions (1994) (16)
From Self-Similarity to Fractional Derivative of Non-Differentiable Functions via Mittag-Leffler Function (2008) (15)
A Minkowskian theory of observation: Application to uncertainty and fuzziness (1987) (15)
Derivation of an amplitude of information in the setting of a new family of fractional entropies (2012) (14)
Fractional multiple birth-death processes with birth probabilities λi(Δt)α+o((Δt)α) (2010) (14)
Fractionalization of the complex-valued Brownian motion of order n using Riemann-Liouville derivative. Applications to mathematical finance and stochastic mechanics (2006) (14)
Solution of the multivariate Fokker-Planck equation by using a maximum path entropy principle (1990) (12)
Tracking control of non-linear stochastic systems by using path cross-entropy and Fokker-Planck equation (1992) (12)
RIEMANN-CHRISTOFFEL TENSOR IN DIFFERENTIAL GEOMETRY OF FRACTIONAL ORDER APPLICATION TO FRACTAL SPACE-TIME (2013) (12)
The Leibniz Rule for Fractional Derivatives Holds with Non-Differentiable Functions (2013) (12)
STOCHASTICS OF ORDER n IN BIOLOGICAL SYSTEMS: APPLICATIONS TO POPULATION DYNAMICS, THERMODYNAMICS, NONEQUILIBRIUM PHASE AND COMPLEXITY (2003) (12)
Further Results on the Modelling of Complex Fractals in Finance, Scaling Observation and Optimal Portfolio Selection (2002) (12)
A New Approach to Fractional Brownian Motion of Order n Via Random Walk in the Complex Plane (1999) (11)
Path probability of random fractional systems defined by white noises in coarse-grained time. Application of fractional entropy (2011) (11)
A new approach to complex-valued fractional Brownian motion via rotating white noise (1998) (11)
THE CONCEPT OF STRUCTURAL ENTROPY AND ITS APPLICATIONS TO GENERAL SYSTEMS (1979) (10)
Nonlinear filtering. A weighted mean squares approach and a Bayesian one via the maximum entropy principle (1990) (10)
Path integral for the probability of the trajectories generated by fractional dynamics subject to Gaussian white noise (2007) (10)
Self‐organization via the creation of constraints: an information theoretic approach (1995) (9)
A norandom variational approach to stochastic linear quadratic Gaussian optimization involving fractional noises (FLQG) (2005) (9)
An Approach to Encoding In the Presence of Subjectivity (1980) (9)
A relativistic information theory model for general systems Lorentz transformation of organizability and structural entropy (1975) (9)
A new information theoretic approach to the entropy of non-random discrete maps relation to fractal dimension and temperature of curves (1997) (9)
Complex-valued Wiener measure: An approach via random walk in the complex plane (1999) (9)
Subjectivity, information, systems : an introduction to a theory of relativistic cybernetics (1986) (8)
FRACTIONAL EULER'S INTEGRAL OF FIRST AND SECOND KINDS. APPLICATION TO FRACTIONAL HERMITE'S POLYNOMIALS AND TO PROBABILITY DENSITY OF FRACTIONAL ORDER (2010) (8)
New results on the entropy of deterministic maps: applications to Liapunov exponent, divergence, compositional inference, and pattern encoding (1988) (8)
Expert Systems and Fuzzy Systems: A New Approach via Possibility‐Probability Conversion (1993) (8)
Towards a new approach to self-organizing systems † (1973) (7)
Oscillation of Non-Linear Systems Close to Equilibrium Position in the Presence of Coarse-Graining in Time and Space (2009) (7)
Fractional Brownian motion with complex variance via random walk in the complex plane and applications (2000) (7)
Tracking control of mechanical systems via sliding Lagrangian (1995) (7)
ON SOME SIMILARITIES AND DIFFERENCES BETWEEN FRACTIONAL PROBABILITY DENSITY SIGNED MEASURE OF PROBABILITY AND QUANTUM PROBABILITY (2009) (7)
Analysis of the equilibrium positions of nonlinear dynamical systems in the presence of coarse-graining disturbance in space (2010) (7)
Simple general method to analyse the moment stability and sensitivity of non-linear stochastic systems with or without delay (1988) (7)
Input-Output Stability Criteria for a Broad Class of Stochastic Nonlinear Distributed Systems Defined by Green’s Function (1975) (6)
Renyi entropy of maps: applications to fuzzy sets, pattern recognition, and chaotic dynamics (1988) (6)
Subjective observation via informational invariance results in creation of fractals and self-similar processes of fractional order (2010) (6)
Stock exchange dynamics involving both Gaussian and Poissonian white noises: approximate solution via a symbolic stochastic calculus (2002) (6)
Would dynamic systems involving human factors be necessarily of fractal nature (2002) (6)
Generalization of the diffusion equation by using the maximum entropy principle (1985) (6)
Image processing via entropies of deterministic functions (1991) (6)
The Price of Granularity and Fractional Finance (2015) (6)
FURTHER RESULTS ON POSSIBILITY-PROBABILITY CONVERSION VIA RELATIVE INFORMATION AND INFORMATIONAL INVARIANCE (1995) (6)
A Theory of Information for Vague Concepts. Outline of Application to Approximate Reasoning (1990) (6)
Trajectory control of manipulators with time varying inertia links (1988) (6)
Informational Entropy of Distributed Deterministic Maps: Applications to Small Samples of Fuzzy Sets and to Pattern Recognition (1989) (5)
On the use of time-varying inertia links to increase the versatility of manipulators (1986) (5)
Improvement of stochastic neighbouring-optimal control using nonlinear Gaussian white noise terms in the Taylor expansions (1996) (5)
Tracking control of flexible robot manipulators with active inertia links (1990) (5)
A new approach to optimum state estimation in optimum system control (1975) (5)
New results in the information theory of patterns and forms (1988) (5)
A practical approach to nonlinear estimation by using the maximum entropy principle (1986) (5)
Structural entropy, information potential, information balance and evolution in self-organizing systems† (1974) (5)
Extension of quantum information by using entropy of deterministic functions (1991) (4)
New approach to control and filtering of mechanical systems by using the estimates of their Lagrangians (1991) (4)
An Approach, Via Entropy, to the Stability of Random Large-Scale Sampled-Data Systems Under Structural Perturbations (1982) (4)
Quantum entropies of nonprobabilistic matrices (1991) (4)
Possibility, probability and relative information: a unified approach via geometric programming (1995) (4)
ENTROPY OF MARKOVIAN PROCESSES : APPLICATION TO IMAGE ENTROPY IN COMPUTER VISION (1998) (4)
A relativistic approach to modelling dynamic systems involving human factors (1979) (4)
Approximate solution for some stochastic differential equations involving both Gaussian and Poissonian white noises (2003) (4)
A General Paradigm for Subjectivity in Communication, Subjective Trausinformation and Subjective Transuncertainty (1981) (4)
Mean-square criteria for the stability of non-linear distributed parameter systems† (1973) (4)
On the effects of random time in dynamical systems (2000) (3)
New results in relativistic information theory. Application to deterministic, stochastic and biological systems† (1976) (3)
A family of geometrical entropies for stochastic processes in path space (1992) (3)
Extension of Gatlin's Informational Divergence to Markovian Stochastic Processes (1997) (3)
Five decades of information theory: successes, disappointments, prospects (1996) (3)
On the use of deformation matrices in artificial vision Systems (1988) (3)
Information theory of deterministic functions. Some new applications to systems analysis (1990) (3)
Informational similarity of graphs in syntactic pattern recognition (1994) (3)
A practical criterion for the input-output stability of distributed parameter systems with space-dependent coefficients† (1975) (3)
Analysis of moment stability and sensitivity of non-linear stochastic distributed systems: a practical approach via a distributed Fokker-Planck equation (1989) (3)
NEW DECISION RULES IN STATISTICAL PATTERN RECOGNITION (1987) (3)
On the consistency between thermodynamic entropy, informational entropy and relativistic information (1984) (2)
Risk and Complex Fractals in Finance∶ Application to a Black-Scholes Equation of Order n (2002) (2)
New methods in artificial vision by using entropies of deterministic functions (1992) (2)
Space Sampling Effects in Nonlinear Distributed System Stability (1981) (2)
Random time-dependent Brownian motion a new approach to fractals of order n (2002) (2)
Solution of the Fokker Plank-Kolmogorov Equation by Using The Maximum Entropy Principle (1985) (2)
Distributed modelling of deterministic and stochastic population dynamics (1986) (2)
Information of deterministic functions and quantum information of non probabilistic matrices A unified approach and new results (1993) (2)
A small parameter method to improve optimum control via the linearization technique (1985) (2)
Information theoretic analysis of distributed systems; a practical approach (1981) (2)
Formal calculus for real‐valued fractional Brownian motions prospects in systems science (2006) (2)
A Model of Positive and Negative Information in thé Standard Framework of Communication Theory — Application to Encoding (1984) (2)
From Entropy of Fuzzy Sets to Fuzzy Set of Entropies: A Critical Review and New Results (1992) (2)
Contour detection by using information theory of deterministic functions (1991) (2)
A concept of observed weighted entropy and its application to pattern recognition (1987) (2)
New Concepts in Information Theory (1987) (2)
Stability Criteria for Distributed Nonlinear Sampled-Data Systems Defined by Green’s Functions (1974) (1)
Complex-Valued Fractional Brownian Motion of Order n. Part I (2000) (1)
An approach to differential geometry of fractional order via modified Riemann-Liouville derivative (2012) (1)
A Survey of Relativistic Information and Its Applications (1977) (1)
Randomization of transfer functions in control systems via computer vision with pixel noises of order n (2001) (1)
A general approach to approximate reasoning via probability-possibility conversion (1993) (1)
Relativistic fuzzy sets. Toward a new approach to subjectivity in human systems (1980) (1)
Stochastic fractional dynamics in the phase plane I. complex-valued noises of order n (1998) (1)
Coordination Concepts in Multilevel Hierarchical Differential Games (1977) (1)
Generalized Fokker-Planck equation for a class of stochastic dynamical systems driven by additive Gaussian and Poissonian fractional white noises of order α (2008) (1)
Mixed Theories of Information can be Derived by Using Shannon Information Only (1986) (1)
Tracking control of manipulators with active inertias by using sliding lagrangian (1996) (1)
Further applications of the non-stationary operational calculus to the synthesis of closed-loop distributed systems A new approach to distributed white noise† (1977) (1)
Informational divergence without probability for patterns and forms (1989) (1)
Further results on the mathematical relations between probability, possibility and fuzzy logic. The rationale of subjectivity via invariance of information loss (1997) (1)
Mixed theories of information can be thought of as direct consequences of relativistic information theory (1986) (1)
An approach to the entropy of ( A or B ) via maximization of conditional entropy (1992) (1)
Image Processing. A new Approach via Informational Entropy and Informational Divergence of non Random Functions (2015) (1)
Probability density of the complex-valued fractional Brownian motion of order n via the maximum entropy principle in R+1/n (2004) (1)
An approach via state estimation to differential games with information time lag (1973) (1)
A Theory of Relative Information (1990) (1)
On the use of invariance properties in observation theory. Application to fuzziness and information (1985) (1)
OBSERVATION WITH INFORMATIONAL INVARIANCE: INTRODUCTION TO A NEW MODELING OF FUZZY ARITHMETICS (1987) (1)
Stability circle criterion with spatial harmonic linearisation for nonlinear distributed-parameter systems (1972) (1)
Towards a mathematical theory of autopoiesis (1987) (1)
A Critical Review of Shannon Information Theory (1990) (1)
Sub-optimal control with observer of a two-lane highway traffic flow† (1981) (1)
A Space Function Approach to the Hyperstability and the Average Hyperstability of Distributed Systems With Space-Varying Linear Parts and Time-Varying Gains (1975) (1)
Hyperstability and average hyperstability conditions for a broad class of gaussian stochastic systems (1979) (1)
Can we use complex-valued fractional Brownian motion to derive a fractal space-time theory in micro-physics (2001) (1)
Composition laws for entropy and temperature in tree-like graphs (1993) (1)
Total Entropy. A Unified Approach to Discrete Entropy and Continuous Entropy (1986) (1)
Two–Stages Sliding Controller for Manipulators with Time–Varying Inertia Links (1989) (1)
Forces of reaction and neighbouring Hamilton's principle in the tracking control of manipulators via a sliding scheme (1993) (1)
On some problems related to linear systems subject to squared white noises (1983) (1)
On the modelling of stochastic differential equations subject to squared white noises (1996) (0)
Scaling observation with complex‐valued coefficients: some remarks and prospects (2002) (0)
A Unified Approach to Informational Entropies via Minkowskian Observation (1990) (0)
An approach via the central limit theorem to randomization of Fourier’s transform (1999) (0)
Use of the quantum entropy of non-probabilistic matrices in automatic control (1993) (0)
Information, Renyi Entropy, H-Convergence, H-Stability. Applications to Identification and Parameter Estimation (1982) (0)
LINEAR SYSTEMS SUBMITTED TO NONLINEAR TRANSFORMATIONS OF GAUSSIAN PROCESSES A RITZ-GALERKIN APPROACH (1984) (0)
Some Approaches to the Specific Problems which Occur in the Optimum Control of the Economies of Developing Young Countries (1977) (0)
Information Theory — The State of the Art (1990) (0)
Fractals, Path Entropy, and Fractional Fokker-Planck Equation (2000) (0)
An embedding approach to the stability of some nonlinear discrete systems (1981) (0)
Path Entropies of Random Functions and of Non-Random Distributed Functions (2000) (0)
Optimal taxation in national economies. Net income entropy, weighted incomes-inequalities and fuzzy saving propensities (2005) (0)
Conjectures on the use of the special relativity in control theory (1980) (0)
Towards an approach to stochastic adaptive control using the maximum entropy principle (1990) (0)
Comment on “Time optimal control of linear systems with delay” and “Optimal control for systems which include pure delays” (1971) (0)
ON THE PROBLEM OF THE MATHEMATICAL THEORIZATION OF HUMAN SYSTEMS DYNAMICS (1981) (0)
Transfer of Entropy in Dynamical Systems—Application to Stochastic Stability (1985) (0)
Information and Self-organization Revisited via Complex-valued Fractional Brownian Motion of Order N (1999) (0)
A New Class of P.I.D. Parameter Adaptation Algorithms for Robot Manipulators (1991) (0)
Further Results on the Application of Entropies of Deterministic Functions to Information of Fuzzy Sets and Related Topics (1991) (0)
Towards a Theory of Distributed Statistical Decision Involving Subjective Factors (1988) (0)
New results on stochastic systems excited by white noise powers (1989) (0)
Path entropies of brightness functions and fractional Brownian motions (1992) (0)
Maximum Entropy Principle, Information of Non-Random Functions and Complex Fractals (2003) (0)
Fuzzy set algebra revisited: a new approach via Renyi entropy of random variables (1997) (0)
Summary of Information Theory (2000) (0)
Informational entropy of non-random non-differentiable functions. An approach via fractional calculus (2015) (0)
Identification of Stochastic Systems by using the Maximum Entrophy Principle (1985) (0)
A Theory of Subjective Information (1990) (0)
Analysis of Nonlinear Stochastic Distributed Systems by using the Dynamic Equations of their State Moments (1987) (0)
Quantum Entropies of Non-Probabilistic Square Matrices (2000) (0)
Information and self‐organization ‐ a new approach via self‐divergence of Markovian processes (1998) (0)
MODELING FRACTAL DYNAMICAL SYSTEMS IN THE COMPLEX SPACE. FROM MACRO-OBSERVATION TO MICRO-OBSERVATION (2002) (0)
Entropy of Form and Pattern (1990) (0)
Structural entropies of order s and of order ( r,s ) for deterministic functions with an application of fuzzy set theory (1990) (0)
Elements for a theory of fractals in dynamic systems involving human factors (1999) (0)
On the non-differentiability of the solutions of the fractional differential equation y^{(\alpha)}(x)=\lambda y(x) (2016) (0)
Research group on relative information and its applications (1988) (0)
Structural sliding equations for the tracking control of mechanical systems with active structure (1996) (0)
About the convergence of the method of the ‘reactive energy minimization principle’† (1970) (0)
Relativistic Information and Biology (1985) (0)
Catastrophe, Chaos, Synergetics and Thermodynamics. A Unified Approach via Information of Deterministic Maps (1988) (0)
A New Family of Fuzzy Set Algebras Derived from Information Theory (1997) (0)
A Theory of Relative Statistical Decision (1990) (0)
POLEMICS IN SYSTEMS RESEARCH (1992) (0)
Outline of Applications (2000) (0)
Stochastic Hamilton's principle and noisy sliding surfaces in the tracking control of manipulators (1995) (0)
Sensitivity analysis of SISO control systems using Wigner distribution (1996) (0)
A New Approach to the Complexity of General Systems via Entropy and Quantum Entropy of Non‐probabilistic Data (1993) (0)
Stability, structural stability, and games: Toward a theory of differential hypergames (1977) (0)
Path Entropies of Non-Random Functions (2000) (0)
Maximum Entropy Principle in Fields of Probabilities. Application to Self-organizing Systems (1997) (0)
Information and quantum information of deterministic data with applications to systems analysis (1992) (0)
A Unified Approach to Discrete and Continuous Entropy (1990) (0)
Further results on the modelling and the control of stochastic dynamics subject to fractional Brownian motion inputs (1994) (0)
A New Approach to Introducing Semantics and Subjectivity in Approximate Reasoning (1988) (0)
A new formulation of the describing function method for non-linear systems subject to stochastic input † (1971) (0)
An Approach to Estimation and Identification Based on Information Theory of Deterministic Functions (1989) (0)
Information Thermodynamics and Complex-Valued Fractional Brownian Motion of Order n (2000) (0)
Stochastic dynamics and fractional white noise in the complex plane—further results and outline of applications (1999) (0)
Concluding Remarks and Outlook (1990) (0)
Urban two-lane highway with quasi-dense traffic: analysis, finite element modelling, perturbation method and optimal control† (1982) (0)
Subjective Information and Limits in Learning Processes Without Teachers (1982) (0)
SOME METHODS FOR ANALYZING THE STABILITY AND THE HYPERSTABILITY OF DISTRIBUTED PARAMETER SYSTEMS (1982) (0)
Analysis of nonlinear discrete systems using the normal form method (1985) (0)
Comparison of Hamiltonians. A new tool for the analysis and the design of deterministic and stochastic dynamical systems (1995) (0)
Optimum control of deterministic and stochastic distributed populations with intra-species competition† (1986) (0)
Applications of Entropy of Patterns and Forms to Signal Processing (1990) (0)

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Guy Jumarie's Academic­Influence.com Rankings

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Guy Jumarie's AcademicInfluence.com Rankings