# Dumitru BaleanuInstitute of Space Sciences

Dumitru Baleanu

PhD

## About

2,236

Publications

469,582

Reads

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64,669

Citations

Citations since 2017

Introduction

Additional affiliations

January 2007 - December 2009

January 2005 - December 2012

January 2001 - December 2013

Education

June 2006

**Institute of Space Sciences**

Field of study

- Physics

May 2001 - June 2006

**Institute of Space Sciences**

Field of study

- Physics

October 1990 - July 1996

**Institute of Atomic Physics**

Field of study

- Theoretical Physics

## Publications

Publications (2,236)

This paper focuses on the study of convexity analysis for discrete delta Riemann-Liouville fractional differences analytically and numerically. In the analytical part of this paper, we will give a new formula for the discrete delta Riemann-Liouville fractional difference as an alternative definition. A formula for the $\Delta^{2}$ will be establish...

Malaria is a deadly human disease that is still a major cause of casualties worldwide. In this work, we consider the fractional-order system of malaria pestilence. Further, the essential traits of the model are investigated carefully. To this end, the stability of the model at equilibrium points is investigated by applying the Jacobian matrix techn...

In this study, we are concerned with the dynamics of a new established fractional-order delayed zooplankton–phytoplankton system. The existence and uniqueness of the solution are proved via Banach fixed point theorem. Non-negativeness of the solution is studied by mathematical inequality technique. The boundedness of the solution is analyzed by vir...

A generalized differential operator utilizing Raina's function is constructed in light of a certain type of fractional calculus. We next use the generalized operators to build a formula for analytic functions of type normalized. Our method is based on the concepts of subordination and superordination. As an application, a class of differential equa...

We show that a class of fractional differences with Mittag-Leffler kernel can be negative and yet monotonicity information can still be deduced. Our results are complemented by numerical approximations. This adds to a growing body of literature illustrating that the sign of a fractional difference has a very complicated and subtle relationship to t...

This paper is concerned with the existence of the solution to mixed-type non-linear fractional functional integral equations involving generalized proportional (κ,ϕ)-Riemann–Liouville along with Erdélyi–Kober fractional operators on a Banach space C([1,T]) arising in biological population dynamics. The key findings of the article are based on theor...

In this paper, we will discuss the monotone decreasing and increasing of a discrete nonpositive and nonnegative function defined on N_{r_0+1} , respectively, which come from analysing the discrete Riemann-Liouville differences together with two necessary conditions (see Lemmas 2.1 and 2.3). Then, the relative minimum and relative maximum will be ob...

The perturbed KdV equation has many applications in mechanics and sound propagation in fluids. The aim of this manuscript is to study novel crucial exact solutions of the generalized perturbed KdV equation. The Hirota bilinear technique is implemented to derive general form solution of the considered equation. The novel soliton solutions are studie...

2021 Best paper award from CMES journal

In this study, we analyse the behaviour of the coinfection of the HIV-TB model using a piecewise operator in the classical-Caputo sense. For the aforementioned disease model, we present the existence as well as the uniqueness of a solution having a piecewise derivative. We also study the different versions of stability using Ulam–Hyers stability in...

Complex problems in nonlinear dynamics foreground the critical support of artificial phenomena so that each domain of complex systems can generate applicable answers and solutions to the pressing challenges. This sort of view is capable of serving the needs of different aspects of complexity by minimizing the problems of complexity whose solutions...

In this article, we investigate the existence of mild solutions and the controllability of a class of nonlinear fractional evolution integrodifferential equations in Banach spaces. To reach the conclusions, the Banach contraction mapping principle, the measure of noncompactness, the theory of resolvent operators, and the fixed point theorems are us...

Forecasting household assets provides a better opportunity to plan their socioeconomic activities for the future. Fractional mathematical models offer to model the asset-holding data into a piece of scientific evidence in addition to forecasting their future value. This research focuses on the development of a new fractional mathematical model base...

In this paper, the ABC fractional derivative is used to provide a mathematical model for the dynamic systems of substance addiction. The basic reproduction number is investigated, as well as the equilibrium points' stability. Using fixed point theory and nonlinear analytic techniques, we verify the theoretical results of solution existence and uniq...

We consider the positivity of the discrete sequential fractional operators $\left(\prescript{\rm RL}{a_{0}+1}\nabla^{\nu_{1}}\,\prescript{\rm RL}{a_{0}}\nabla^{\nu_{2}}{f}\right)(\tau)$ defined on the set $\mathscr{D}_{1}$ (see \eqref{setD1} and Figure \ref{fig:1}) and $\left(\prescript{\rm RL}{a_{0}+2}\nabla^{\nu_{1}}\,\prescript{\rm RL}{a_{0}}\na...

The perturbed nonlinear Schrödinger (NLS) equation and the nonlinear radial dislocations model in microtubules (MTs) are the underlying frameworks to simulate the dynamic features of solitons in optical fibers and the functional aspects of microtubule dynamics. The generalized Kudryashov method is used in this article to extract stable, generic, an...

In this paper, we introduce new types of additive functional equations and obtain the solutions to these additive functional equations. Furthermore, we investigate the Hyers-Ulam stability for the additive functional equations in fuzzy normed spaces and random normed spaces using the direct and fixed point approaches. Also, we will present some app...

Several numerical techniques for solving initial value problems arise in physical and natural sciences. In many cases, these problems require numerical treatment to achieve the required solution. However, in today’s modern era, numerical algorithms must be cost-effective with suitable convergence and stability features. At least the fifth-order con...

The aim of this research is to present an investigation based on the fractional derivatives and perturbation factors for the novel singular system. This study also presents a novel design of the fractional perturbed singular system by using the conventional Lane-Emden form together with the features of fractional order values, singular points, pert...

In this paper, we propose a general formulation for the transmission dynamics of maize streak virus (MSV) pathogen interaction with a pest invasion in the maize plant. The mathematical formalism for this model is dependent on Caputo fractional operator with modification of its parameters. In the considered model, the total population of maize plant...

In many of our real life problems, we often come across situations where there is no information about the priority weights which make it difficult to analyze the objects under consideration. Instead of employing simple fuzzy sets, “interval type-2 trapezoidal pythagorean fuzzy preference relations (IT2TrPFPRs)” can be used which have better repres...

In this relativistic consideration, the energy integral unlike others has been derived in a weakly relativistic plasma in terms of Sagdeev potential. Both compressive and rarefactive subsonic solitary waves are found to exist, depending on wave speeds in various directions of propagation. It is found that compressive relativistic solitons have pote...

Throughout this article, generalizations of some Grónwall–Bellman integral inequalities for two real-valued unknown functions in n independent variables are introduced. We are looking at some novel explicit bounds of a particular class of Young and Pachpatte integral inequalities. The results in this paper can be utilized as a useful way to investi...

The vital target of the current work is to construct two-variable Vieta-Fibonacci polynomials which are coupled with a matrix collocation method to solve the time-fractional telegraph equations. The emerged fractional derivative operators in these equations are in the Caputo sense. Telegraph equations arise in the fields of thermodynamics, hydrolog...

The main purpose of the current paper is to establish a (4 + 1)-dimensional nonlinear evolutionary (4D-NLE) equation and derive its Bäcklund transformation, complexiton, and solitons. To this end, the Bäcklund transformation of the 4D-NLE equation is first constructed by applying the truncated Painlevé expansion. The simplified Hirota’s method is t...

The purpose of this study is to employ the Sine–Cosine expansion approach to produce some new sort of soliton solutions for the cubic–quintic nonlinear Helmholtz problem. The nonlinear complex model compensates for backward scattering effects that are overlooked in the more popular nonlinear Schrödinger equation. As a result, a number of novel trav...

This study establishes the extended classical optical solitons for a nonlinear Schrodinger equation describing resonant nonlinear light propagation through isolated flaws in optical wave guides. We use the modified Sardar sub-equation approach to get such innovative results. The innovative optical solitons solutions have been investigated to explai...

This research proposes a method to find numerical solutions of the variable-order fractional differential equation. We derived new operational matrix by applying Bernstein polynomials. Then, using this matrix, the method of solving the system of variable-order fractional differential equation and variable-order fractional partial differential equat...

The applications of the diffusion wave model of a time-fractional kind with damping and reaction terms can occur within classical physics. This quantification of the activity can measure the diagnosis of mechanical waves and light waves. The goal of this work is to predict and construct numerical solutions for such a diffusion model based on the un...

Fractional calculus approach, providing novel models through the introduction of fractional-order calculus to optimization methods, is employed in machine learning algorithms. This scheme aims to attain optimized solutions by maximizing the accuracy of the model and minimizing the functions like the computational burden. Mathematical-informed frame...

The magnetohydrodynamics boundary layer flow of rate type fluid over an oscillating inclined infinite plate along with Newtonian heating and slip at the boundary is investigated. The model is developed by using the Atangana-Baleanu time-fractional derivative operator. Temperature and velocity fields for the non-integer order derivative model are co...

Fractional calculus approach, providing novel models through the introduction of fractional-order calculus to optimization methods, is employed in machine learning algorithms. This scheme aims to attain optimized solutions by maximizing the accuracy of the model and minimizing the functions like the computational burden. Mathematical-informed frame...

We investigate the initial-boundary value problems for a fourth-order differential equation within the powerful fractional Dzherbashian-Nersesian operator (FDNO). Boundary conditions considered in this manuscript are of the Samarskii-Ionkin type. The solutions obtained here are based on a series expansion using Riesz basis in a space corresponding...

In this manuscript, we implement a spectral collocation method to find the solution of the reaction–diffusion equation with some initial and boundary conditions. We approximate the solution of equation by using a two-dimensional interpolating polynomial dependent to the Legendre–Gauss–Lobatto collocation points. We fully show that the achieved appr...

In machine learning models, one of the most popular models is artificial neural networks. The activation function is one of the important parameters of neural networks. In this paper, the sigmoid function is used as an activation function with a fractional derivative approach to minimize the convergence error in backpropagation and to maximize the...

The Fermatean fuzzy set has been authorized as a suitable tool for the uncertainty and vagueness of information by augmenting the spatial space of acceptance membership and non-acceptance membership degrees of both intuitionistic and Pythagorean fuzzy sets. Solar energy does not emit any hazardous gases into the atmosphere, making it one of the mos...

Introduction
Recently, a new family of fractional derivatives called the piecewise fractional derivatives has been introduced, arguing that for some problems, each of the classical fractional derivatives may not be able to provide an accurate statement of the consideration problem alone. In defining this kind of derivatives, several types of fracti...

In the present article, we geometrically and analytically examine the mutual impact of space-time Caputo derivatives embedded in (1 + 2)-physical models. This has been accomplished by integrating the residual power series method (RPSM) with a new trivariate fractional power series representation that encompasses spatial and temporal Caputo derivati...

Coronavirus Disease 2019 (COVID-19), a new illness caused by a novel coronavirus, a member of the corona family of viruses, is currently posing a threat to all people, and it has become a significant challenge for healthcare organizations. Robotics are used among other strategies, to lower COVID’s fatality and spread rates globally. The robot resem...

This work employs a novel variation of the Sardar sub-equation approach to investigate the optical solitons for the nonlinear Hirota-Schrodinger equation. Different soliton solutions, including bright solitons, dark solitons, singular solitons, combined bright-singular solitons, periodic, exponential, and rational solutions are derived along with n...

The principal goal of the presented paper is to investigate the dynamics of optical solitons for the generalized Sasa–Satsuma (GSS) equation describing the propagation of the femtosecond pulses in the systems of optical fiber transmission. More precisely, the governing model, which is a generalized version of the classical Sasa–Satsuma equation, is...

The objective of this paper is to prove some new dynamic inequalities of Hardy type on time scales which generalize and improve some recent results given in the literature. Further, we derive some new weighted Hardy dynamic inequalities involving many functions on time scales. As special cases, we get continuous and discrete inequalities.

This paper concerns with the existence, uniqueness, Ulam’s Hyer (UH) stability and total controllability results for the Hilfer fractional switched impulsive systems in finite-dimensional spaces. Mainly, this paper can be divided into three parts. In the first part, we examine the existence of a unique solution. In the second part, we establish the...

We prove some new dynamic inequalities of the Gronwall–Bellman–Pachpatte type on time scales. Our results can be used in analyses as useful tools for some types of partial dynamic equations on time scales and in their applications in environmental phenomena and physical and engineering sciences that are described by partial differential equations.

The utilization of solar energy is essential to all living things since the beginning of time. In addition to being a constant source of energy, solar energy (SE) can also be used to generate heat and electricity. Recent technology enables to convert the solar energy into electricity by using thermal solar heat. Solar energy is perhaps the most eas...

In this paper, we formulate a new model of a particular type of influenza virus called AH1N1/09 in the framework of the four classes consisting of susceptible, exposed, infectious and recovered people. For the first time, we here investigate this model with the help of the advanced operators entitled the fractal–fractional operators with two fracta...

This paper is devoted to identifying an unknown source for a time-fractional diffusion equation in a general bounded domain. First, we prove the problem is non-well posed and the stability of the source function. Second, by using the Modified Fractional Landweber method, we present regularization solutions and show the convergence rate between regu...

In this paper, a novel variable-order COVID-19 model with modified parameters is presented. The variable-order fractional derivatives are defined in the Caputo sense. Two types of variable order Caputo definitions are presented here. The basic reproduction number of the model is derived. Properties of the proposed model are studied analytically and...

In this work, the distributed-order fractional version of the Schrödinger problem is defined by replacing the first order derivative in the classical problem with this kind of fractional derivative. The Caputo fractional derivative is employed in defining the used distributed fractional derivative. The orthonormal piecewise Jacobi functions as a no...

In this article, we extend the generalized invexity and duality results for multiobjective variational problems with fractional derivative pertaining to an exponential kernel by using the concept of weak minima. Multiobjective variational problems find their applications in economic planning, flight control design, industrial process control, contr...

This paper will focus on determining the approximate numerical solutions for several types of linear and nonlinear Ordinary differential equations. This solution is based on the direct numerical technique, which depends on the Legendre polynomials' derivatives. Then, we will give an approximate solution as a finite sum of the polynomials and unknow...

We established several novel inequalities of Gronwall–Pachpatte type on time scales. Our results can be used as handy tools to study the qualitative and quantitative properties of the solutions of the initial boundary value problem for a partial delay dynamic equation. The Leibniz integral rule on time scales has been used in the technique of our p...

In this article, with the help of Leibniz integral rule on time scales, we prove some new dynamic inequalities of Gronwall–Bellman–Pachpatte-type on time scales. These inequalities can be used as handy tools to study the qualitative and quantitative properties of solutions of the initial boundary value problem for partial delay dynamic equation.

This paper investigates a tumor-macrophages interaction model with a discrete-time delay in the growth of pro-tumor M2 macrophages. The steady-state analysis of the governing model is performed around the tumor dominant steady-state and the interior steady-state. It is found that the tumor dominant steady-state is locally asymptotically stable unde...

Fractals, as a universal language, are often considered to be an abundant source of creativity, surprise, beauty and reality. Being regarded and employed as a powerful tool to communicate, interpret, describe and analyze complex ideas and complexity in nature and other imaginable systems, fractals can most of the time remind one of a story or a nar...

In this paper, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory are re-stated. Then, the addition of velocity laws are derived and used to verify the constancy of the speed of light. The invariance principle of the laws of physics is demonstrated fo...

A new generalized KdV equation, describing the motions of long waves in shallow water under the gravity field, is considered in this paper. By adopting a series of well-organized methods, the Bäcklund transformation, the bilinear form and diverse wave structures of the governing model are formally extracted. The exact solutions listed in this paper...

The major goal of the present paper is to construct optical solitons of the Ginzburg–Landau equation including the parabolic nonlinearity. Such an ultimate goal is formally achieved with the aid of symbolic computation, a complex transformation, and Kudryashov and exponential methods. Several numerical simulations are given to explore the influence...

The breather wave and lump periodic wave solutions for the (2+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2+1$$\end{document})-dimensional Caudrey–Dodd–Gibbon–Kote...

Legendre polynomials’ first derivatives have been used as the basis function via the pseudo-Galerkin spectral method. Operational matrices for derivatives have been used and extended to deal with the system of ordinary differential-algebraic equations. An algorithm via those matrices has been designed. The accuracy and efficiency of the proposed al...

In this article, using a (γ,a)-nabla conformable integral on time scales, we study several novel Hilbert-type dynamic inequalities via nabla time scales calculus. Our results generalize various inequalities on time scales, unifying and extending several discrete inequalities and their corresponding continuous analogues. We say that symmetry plays a...

The main goal of this manuscript is to investigate a fractional optimal control problem subject to a dynamical system involving Hadamard fractional derivatives. Necessary conditions for the optimality of the considered problem are derived in terms of the corresponding Euler–Lagrange equations. An iterative method is also proposed to numerically sol...

In this study, we have presented two new alternative definitions corresponding to the basic definitions of the discrete delta and nabla fractional difference operators. These definitions and concepts help us in establishing a relationship between Riemann-Liouville and Liouville-Caputo fractional differences of higher orders for both delta and nabla...

In this study, a dimensionally nonlinear evolution equation, which is the integrable shallow water wave-like equation, is investigated utilizing the Hirota bilinear approach. Lump solutions are achieved by its bilinear form and are essential solutions to various kind of nonlinear equations. It has not yet been explored due to its vital physical sig...

Advanced Fractals and Fractional Calculus with Science and Engineering Applications: Computing, Dynamics and Control in Complex Systems

This work addresses a hybrid scheme for the numerical solutions of time fractional Tricomi and Keldysh type equations. In proposed methodology, Haar wavelets are used for discretization in space while θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{m...

Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, c...

In this study, a hot and desert location with an annual temperature of 27.1 °C and a very high radiation intensity of 2143 kWh/m², a solar system (ES) was approved to provide building cooling necessities. The cooling system, by connecting to the solar system, supplied a part of its required energy. The outer layer of the building walls was equipped...