Honorary Speaker

Dumitru Baleanu

Prof. Dumitru Baleanu

Lebanese American University, Department of Computer Science and Mathematics, Beirut, Lebanon

dumitru.baleanu@lau.edu.lb

Speech Title: Some New Directions within Fractional Calculus and Its Applications

 

Abstract:

Fractional order differential equations, that is, those involving real or complex order derivatives, have assumed a very important role in modelling the anomalous dynamics of various processes related to complicated systems in the most diverse fields of science and engineering. In this talk, I will present new generalized fractional operators together with some of their real-world applications.

Biography:

Dumitru Baleanu is a professor at the Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon. Dumitru got his PhD from the Institute of Atomic Physics in 1996. His fields of interest include the fractional dynamics and its applications, fractional differential equations and their applications, discrete mathematics, image processing, bio-informatics, mathematical biology, mathematical physics, soliton theory, Lie symmetry, dynamic systems on time scales, computational complexity, the wavelet method and its applications, quantization of systems with constraints, the Hamilton-Jacobi formalism, geometries admitting generic and non-generic symmetries.

Dumitru is a pioneer of the fractional variational principles and their applications in control theory. Dumitru wrote for the first time the fractional Euler-Lagrange equations for fields in the seminal paper entitled [Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives, D. Baleanu and S. I. Muslih, Physica Scripta ,72 ( 2-3) 119-121(2005)].

Besides, in the following paper entitled [A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems, A. O. Prakash and D. Baleanu, Journal of Vibration and Control 13 (9-10),1269-1281], we firstly formulated the fractional optimal control problems in terms of Riemann-Liouville fractional derivatives.

Together with his collaborators, Dumitru made the first generalisation of the spatial Laplacian in the Bloch-Torrey equation to incorporate a fractional order Brownian model of diffusivity. [R. L. Magin, O. Abdullah, D. Baleanu, X. I. Zhou, Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation, J. Magn. Reson. 190, 255-270 (2008)]. Fractional order dynamic derived from this case was observed to better fit the signal attenuation in diffusion-weighted images obtained from Sephadex gels, human articular cartilage and human brain. Dumitru had an important role in developing the non-singular operators with Mittag-Leffler kernels and the related modified version as well as their applications in real world phenomena.

Also, Dumitru introduced, for the first time, the geometrical meaning of the fractional Mittag-Leffler kernel in the complex domain. This was an open problem in the history of 329 years of the fractional calculus. The results were published in the paper entitled [Modified Atangana-Baleanu fractional differentıal operators, R. W. Ibrahim and D. Baleanu, Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan Volume 48, Special Issue, 2022, 56–67 (2022)].

We know that dealing with nonsingular kernels it is a very difficult task mainly because their unsolved restrictions at origin. However, in the paper entitled [On an extension of the operator with Mittag-Leffler kernel, M. Al-Refai and D. Baleanu, Fractals, 30(51), 2022, Article number 2240129], it was first time formulated an interesting extension of the fractional operator involving the Mittag-Leffler kernel which admits integrable singular kernel at the origin. Besides, new solutions of the related differential equations were reported together with some perspectives from the modelling viewpoint.

Dumitru and his collaborator establish for the first time a formula for the fractional derivative with Mittag-Leffler kernel in the form of a series of Riemann-Liouville fractional integrals and proved the existence and uniqueness results for certain families of linear and nonlinear fractional ODEs with practical applications [D. Baleanu, A. Fernandez, On some new properties of fractional derivatives with Mittag-Leffler kernel, Communications in Nonlinear Science and Numerical Simulation 59, 444-462 (2018)].

Dumitru proposed a new semi-analytical method based on Adomian polynomials and a fractional Taylor series to investigate chaotic behavior and stability of fractional differential equations within anew generalized Caputo derivative [D. Baleanu, G.C. Wu, S.D. Zeng, Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations, Chaos, Solitons and Fractals 102, 99–105 (2017)].

Dumitru obtained pioneering results in the discrete fractional calculus regarding the monotonicity properties of the Caputo and the right fractional differences [T. Abdeljawad, D. Baleanu, Monotonicity analysis of a nabla discrete fractional operator with discrete Mittag-Leffler kernel, Chaos, Solitons and Fractals 102, 106–110 (2017)].

Dumitru contributes to generalise a fractional time discretization diffusion model using the Caputo-like delta's approach [G.C. Wu, D. Baleanu, S.D. Zeng, Z.G. Deng, Discrete fractional diffusion equation, Nonlinear Dynamics 80, 281-286 (2015)].

Dumitru also contributed to the development of the Weyl–Titchmarsh theory for the still unsolved fractional Sturm–Liouville equation [E. Uğurlu, D. Baleanu, K. Taş, On square integrable solutions of a fractional differential equation, Applied Mathematics and Computation 337, 153–157 (2018)].

In the paper [G.C. Wu, D. Baleanu, Discrete chaos in fractional delayed logistic maps, Nonlinear Dynamics 80 (4), 697-1703 (2015)] it was proposed a new chaotic map with more parameters and complicated chaotic behavior such that the secret space increases in image encryption. The new map generates fast chaotic series and were used to encryption of big data.

In the paper [D. Baleanu, A. Jajarmi, S.S. Sajjadi, D. Mozyrska, A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator, Chaos, Volume 29, Issue 81,2019, Article number 083127] a new optimal control strategy for investigating the effect of chemotherapy treatment on the proposed fractional model is provided. Simulation results show clearly that the new presented model based on the fractional operator with Mittag-Leffler kernel represents various asymptomatic behaviors that tracks the real data more accurately than the other fractional- and integer-order models.

In the paper [On a fractional operator combining proportional and classical differintegrals, D. Baleanu,A. Fernandez, A. Akgul, Mathematics, Volume 8, Issue 31, 2020, Article number 360] we presented two new fractional derivatives with a big impact for the modelling viewpoint. They were first formulated by taking the Caputo fractional derivative and replacing the simple derivative by a derivative of proportional type. They can also be written as a composition of a Riemann–Liouville fractional integral with this proportional-type derivative.

Dumitru is co-author of the following books:

  • M. Hashemi, D. Baleanu, Lie Symmetry Analysis of Fractional Differential Equations, CRC, Press/Taylor & Francis Group, 2020;
  • D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus: Models and Numerical Methods, World Scientific Publishing, 1 st Ed. 2012 and 2 nd Ed. 2016;
  • D. Baleanu, O. Mustafa, Asymptotic Integration and Stability for Differential Equations of Fractional Order, World Scientific Publishing, 2015;
  • X.J. Yang, D. Baleanu, H.M. Srivastava, Local Fractional Integral Transforms and Their Applications, Academic Press – Elsevier, 2015.
Besides, Dumitru is co-author of 23 co-edited books published by various prestigious publishers: American Institute of Physics (1), CRC Press (1), Springer (13), Intechopen (3), Academic Press (3), De Gruyter (2).

Dumitru’s H index is 108 and the number of his citations are 56,815 citations (without self citations) according to Web of Science. Dumitru was Highly Cited Researcher in Mathematics.

Dumitru is affiliated with: Sigma Xi, The Scientific Research Honor Society (2020), African Mathematical Union (2019) and MESA (Mechatronic and Embedded Systems and Applications) (2007).

Dumitru, as a PI or co-PI, won several national and international projects.

Dumitru won the following prestigious awards:
  • 2024 - Biruni Award for lifetime achievement in nonlinear science
  • 2023 - Award Grigore Moisil given by the Romanian Academy
  • 2023 - C.S. Hsu Award, Given for distinguished scholars in Nonlinear Dynamics and Control and presented during the Conference on Nonlinear Science and Complexity, Biruni University, 10-15, July 2023, Istanbul Turkey
  • 2020 - Best Research Award, given by the ITSR Foundation Award 2020 (organized by Institute of Technical and Scientific Research, India) and presented online on September 13th, 2020.
  • 2020 - Distinguished Researcher Award, Given by the Jaipur Mathematical Society and presented during the 3rd International Conference on Mathematical Modelling, Applied Analysis and Computation (ICMMAAC-20),7-9 August 2020 at JECRC University,Jaipur, India
  • 2019 - Award for 20 years of successful scientific activity in the field of fractional calculus and its applications by Istanbul Gelisim University, Turkey
  • 2019 - Obada Prize. The Obada-Prize recognizes and encourages innovative and interdisciplinary research that cuts across traditional boundaries and paradigms. It aims to foster universal values of excellence, creativity, justice, democracy, and progress and to promote the scientific, technological and humanistic achievements that advance and improve our world.
  • 2018 - ICFDA2018 Award: Innovation in Fractional Calculus. This award is granted to inventors of new patents which address major problems and have a great perspective by use of fractional calculus in real World applications.
Dumitru is the Editor in Chief of Progress in Fractional Differentiation and Applications and he is a Co-editor in Chief of Discontinuity, Nonlinearity and Complexity. Dumitru is member of several editorial boards of journals indexed in SCI.