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Mathematics

D-Index
36
Citations
5528
World Ranking
2638
National Ranking
164

Overview

Yuri Luchko is a researcher affiliated with Beuth University of Applied Sciences in Germany, specializing in the field of Mathematics. Their work primarily focuses on fractional calculus and differential equations, with a large body of publications contributing to both theoretical and applied mathematics.

The scientist has published extensively in the main field of Mathematics, with notable contributions to several subfields including Applied Mathematics, Modeling and Simulation, Numerical Analysis, Mathematical Physics, and Mechanics of Materials. Their research encompasses the study and solutions of fractional differential equations, mathematical functions and polynomials, nonlinear differential equations analysis, differential equations and boundary problems, iterative methods for nonlinear equations, numerical methods in engineering, and differential equations alongside numerical methods.

Recent publications by Yuri Luchko include:

  • Trends, directions for further research, and some open problems of fractional calculus (2022) in Nonlinear Dynamics
  • The General Fractional Derivative and Related Fractional Differential Equations (2020) in Mathematics
  • Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann-Liouville Sense (2022) in Mathematics
  • Convolution series and the generalized convolution Taylor formula (2022) in Fractional Calculus and Applied Analysis
  • Special Functions of Fractional Calculus in the Form of Convolution Series and Their Applications (2021) in Mathematics

The researcher has a history of collaboration with several frequent co-authors, including Mohammed Al-Refai, Masahiro Yamamoto, Maryam Al-Kandari, and J. A. Tenreiro Machado. These collaborations have contributed to the development of their research topics and broadened their scope within the field.

Yuri Luchko's work is commonly published in venues such as:

  • Mathematics
  • arXiv (Cornell University)
  • Fractional Calculus and Applied Analysis
  • Preprints.org
  • Axioms

The core topics in their research include:

  • Fractional Differential Equations Solutions
  • Mathematical functions and polynomials
  • Nonlinear Differential Equations Analysis
  • Differential Equations and Boundary Problems
  • Iterative Methods for Nonlinear Equations
  • Numerical methods in engineering
  • Differential Equations and Numerical Methods

Best Publications

  • The fundamental solution of the space-time fractional diffusion equation

    Francesco Mainardi;Yuri Luchko;Gianni Pagnini

  • Wright functions as scale-invariant solutions of the diffusion-wave equation

    Rudolf Gorenflo;Yuri Luchko;Francesco Mainardi

  • Invariance of a Partial Differential Equation of Fractional Order under the Lie Group of Scaling Transformations

    Evelyn Buckwar;Yuri Luchko

  • Analytical properties and applications of the Wright function

    Rudolf Gorenflo;Yuri Luchko;Francesco Mainardi

  • Time-fractional diffusion equation in the fractional Sobolev spaces

    Rudolf Gorenflo;Yuri Luchko;Masahiro Yamamoto

  • The exact solution of certain differential equations of fractional order by using operational calculus

    Yu.F. Luchko;H.M. Srivastava

  • Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation

    Yuri Luchko

  • General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems

    Yuri Luchko;Masahiro Yamamoto

  • Fractional Schrödinger equation for a particle moving in a potential well

    Yuri Luchko

  • Handbook of fractional calculus with applications

    Anatolij N. Kočubej;Yuri Luchko

  • Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density

    Rudolf Gorenflo;Yuri Luchko;Mirjana Stojanović

  • Desiderata for Fractional Derivatives and Integrals

    Rudolf Hilfer;Yuri Luchko

  • Fractional wave equation and damped waves

    Yuri Luchko

  • Trends, Directions for Further Research, and Some Open Problems of Fractional Calculus

    Kai Diethelm;Virginia Kiryakova;Yuri Luchko;J. A. Tenreiro Machado

  • General fractional integrals and derivatives with the Sonine kernels

    Yuri Luchko

  • Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction-diffusion equation

    Yuri Luchko;William Rundell;Masahiro Yamamoto;Lihua Zuo

  • Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations

    Zhiyuan Li;Yuri Luchko;Masahiro Yamamoto

  • The General Fractional Derivative and Related Fractional Differential Equations

    Yuri Luchko;Masahiro Yamamoto

  • Analyticity of solutions to a distributed order time-fractional diffusion equation and its application to an inverse problem

    Zhiyuan Li;Yuri Luchko;Masahiro Yamamoto

  • Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense

    Unknown

  • Operational calculus for the general fractional derivative and its applications

    Yuri Luchko

  • Propagation speed of the maximum of the fundamental solution to the fractional diffusion-wave equation

    Yuri Luchko;Francesco Mainardi;Yuriy Povstenko

  • Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications

    Mohammed Al-Refai;Yuri Luchko

  • The mellin integral transform in fractional calculus

    Yuri Luchko;Virginia Kiryakova

  • General Fractional Integrals and Derivatives of Arbitrary Order

    Yuri Luchko

Frequent Co-Authors

Francesco Mainardi
Francesco Mainardi National Institute for Nuclear Physics
Rudolf Gorenflo
Rudolf Gorenflo Freie Universität Berlin
Masahiro Yamamoto
Masahiro Yamamoto University of Tokyo
J. A. Tenreiro Machado
J. A. Tenreiro Machado Polytechnic Institute of Porto
Pagavathigounder Balasubramaniam
Pagavathigounder Balasubramaniam Gandhigram Rural Institute
Vasily E. Tarasov
Vasily E. Tarasov Lomonosov Moscow State University
William Rundell
William Rundell Texas A&M University
Varsha Daftardar-Gejji
Varsha Daftardar-Gejji Savitribai Phule Pune University
Kai Diethelm
Kai Diethelm Technische Universität Braunschweig

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