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A k-Dimensional System of Fractional Finite Difference Equations
(Hindawi Ltd, 2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid
We investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii's fixed point theorem. We present an example in order to illustrate our results.
About fractional quantization and fractional variational principles
(Elsevier, 2009) Baleanu, Dumitru
in this paper, a new method of finding the fractional Euler-Lagrange equations within Caputo derivative is proposed by making use of the fractional generalization of the classical Fad di Bruno formula. The fractional Euler-Lagrange and the fractional Hamilton equations are obtained within the 1 + 1 field formalism. One illustrative example is analyzed. (C) 2008 Elsevier B.V. All rights reserved.
AN ANALYTICAL STUDY OF (2+1)-DIMENSIONAL PHYSICAL MODELS EMBEDDED ENTIRELY IN FRACTAL SPACE
(Editura ACAD Romane, 2019) Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; Abdel-Muhsen, Ruwa
In this article, we analytically furnish the solution of (2 + 1)-dimensional fractional differential equations, with distinct fractal-memory indices in all coordinates, as a trivariate (alpha, beta, gamma)-fractional power series representation. The method is tested on several physical models with inherited memories. Moreover, a version of Taylor's theorem in fractal three-dimensional space is presented. As a special case, the solutions of the corresponding integer-order cases are extracted by letting alpha, beta, gamma -> 1, which indicates to some extent for a sequential memory.
Citation - WoS: 11
Citation - Scopus: 18
Analysis of the family of integral equation involving incomplete types of I and Ī-functions
(Taylor & Francis Ltd, 2023) Bhatter, Sanjay; Jangid, Kamlesh; Kumawat, Shyamsunder; Baleanu, Dumitru; Suthar, D.L.; Purohit, Sunil Dutt
The present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete (Formula presented.) -function (I (Formula presented.) F) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete (Formula presented.) -function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems.
Chain and Hamilton-Jacobi approaches for systems with purely second class constraints
(Soc Italiana Fisica, 2003) Baleanu, Dumitru; Güler, Y.
The equivalence of the chain method and Hamilton-Jacobi formalism is demonstrated. The stabilization algorithm of Hamilton-Jacobi formalism is clariffied and two examples are presented in details.
Convolution theorems associated with some integral operators and convolutions
(Taylor&Francis LTD, 2019) Al-Omari, Shrideh Khalaf Qasem; Baleanu, Dumitru; Ata, Yalcin; Baykal, Yahya
In this article, various convolution theorems involving certain weight functions and convolution products are derived. The convolution theorems we obtain are more general, convenient, and efficient than the complicated convolution theorem of the Hartley transform. Further results involving new variants of generalizations of Fourier and Hartley transforms are also discussed.
Exact solutions for thermomagetized unsteady non-singularized jeffrey fluid: Effects of ramped velocity, concentration with newtonian heating
(Elsevier, 2021) Aziz-Ur, Rehman; Riaz, Muhammad Bilal; Awrejcewicz, Jan; Baleanu, Dumitru; Aziz-ur-rehman,
The classical calculus due to the fact that it assumed as the instant rate of change of the output, when the input level changes. Therefore it is not able to include the previous state of the system called memory effect. But in the Fractional Calculus (FC), the rate of change is affected by all points of the considered interval, so it is able to incorporate the previous history/memory effects of any system. Due to the importance of this effect we used the modern concept of the Caputo-Fabrizio fractional derivative on the considered Jeffrey fluid model. In this paper the effect of Newtonian heating, concentration and velocity on unsteady MHD free convective flow of Jeffrey fluid over long vertical an infinite ramped wall nested in porous material are discussed. Exact analytical solutions are derived via Laplace transformation technique for principal equations of energy, concentration and ramped velocity. The prime features of various coherent parameters are deliberated and illuminated with the aid of plotted graphs. A comparative study to show the significance of fractional order model with an integer order model is accomplished. The fractional order model is found to be the best choice for explaining the memory effect of the considered problem. It is identified that temperature distribution, concentration and ramped velocity profiles for fractional model are converges to an ordinary model when fractional parameter tends to integer order, which shows that fractional model is more appropriate to explicate experimental results. © 2021
Citation - Scopus: 3
Fractional Gegenbauer Kernel Functions: Theory and Application
(Springer, 2023) Nedaei Janbesaraei, Sherwin; Azmoon, Amirreza; Baleanu, Dumitru
Because of the usage of many functions as a kernel, the support vector machine method has demonstrated remarkable versatility in tackling numerous machine learning issues. Gegenbauer polynomials, like the Chebyshev and Legender polynomials which are introduced in previous chapters, are among the most commonly utilized orthogonal polynomials that have produced outstanding results in the support vector machine method. In this chapter, some essential properties of Gegenbauer and fractional Gegenbauer functions are presented and reviewed, followed by the kernels of these functions, which are introduced and validated. Finally, the performance of these functions in addressing two issues (two example datasets) is evaluated.
Citation - Scopus: 1
Fractional Order Computing and Modeling with Portending Complex Fit Real-World Data
(Springer International Publishing AG, 2023) Karaca, Yeliz; Rahman, Mati ur; Baleanu, Dumitru
Fractional computing models identify the states of different systems with a focus on formulating fractional order compartment models through the consideration of differential equations based on the underlying stochastic processes. Thus, a systematic approach to address and ensure predictive accuracy allows that the model remains physically reasonable at all times, providing a convenient interpretation and feasible design regarding all the parameters of the model. Towards these manifolding processes, this study aims to introduce new concepts of fractional calculus that manifest crossover effects in dynamical models. Piecewise global fractional derivatives in sense of Caputo and Atangana-Baleanu-Caputo (ABC) have been utilized, and they are applied to formulate the Zika Virus (ZV) disease model. To have a predictive analysis of the behavior of the model, the domain is subsequently split into two subintervals and the piecewise behavior is investigated. Afterwards, the fixed point theory of Schauder and Banach is benefited from to prove the existence and uniqueness of at least one solution in both senses for the considered problem. As for the numerical simulations as per the data, Newton interpolation formula has been modified and extended for the considered nonlinear system. Finally, graphical presentations and illustrative examples based on the data for various compartments of the systems have been presented with respect to the applicable real-world data for different fractional orders. Based on the impact of fractional order reducing the abrupt changes, the results obtained from the study demonstrate and also validate that increasing the fractional order brings about a greater crossover effect, which is obvious from the observed data, which is critical for the effective management and control of abrupt changes like infectious diseases, viruses, among many more unexpected phenomena in chaotic, uncertain and transient circumstances.
Improved (G'/G)-expansion method for the time-fractional biological population model and Cahn-Hilliard equation
(ASME, 2015) Baleanu, Dumitru; Uǧurlu, Yavuz; İnç, Mustafa; Kılıç, Bülent
In this paper, we used improved (G'/G)-expansion method to reach the solutions for some nonlinear time-fractional partial differential equations (fPDE). The fPDE is reduced to an ordinary differential equation (ODE) by means of Riemann-Liouille derivative and a basic variable transformation. Various types of functions are obtained for the time-fractional biological population model (fBPM) and Cahn-Hilliard (fCH) equation. Copyright © 2015 by ASME.
Impulsive effects on stability and passivity analysis of memristor-based fractional-order competitive neural networks
(Elsevier, 2020) Rajchakit, G.; Chanthorn, P.; Niezabitowski, M.; Raja, R.; Baleanu, Dumitru; Pratap, A.
This paper analyzes the stability and passivity problems for a class of memristor-based fractional-order competitive neural networks (MBFOCNNs) by using Caputo's fractional derivation. Firstly, impulsive effects are taken well into account and effective analysis techniques are used to reflect the system's practically dynamic behavior. Secondly, by using the Lyapunov technique, some sufficient conditions are obtained by linear matrix inequalities (LMIs) to ensure the stability and passivity of the MBFOCNNs, which can be effectively solved by the LMI computational tool in MATLAB. Finally, two numerical models and their simulation results are given to illustrate the effectiveness of the proposed results. © 2020 Elsevier B.V.
Magnetic Stimulation on Human Blood Electromotive force analysis
(Chiminform Data SA, 2018) Cordova Fraga, Teodoro; Maria Magdaleno, Dulce; Gomez Aguilar, Jose Francisco; Olivia Murillo, Blanca; Sosa, Modesto; Baleanu, Dumitru; Guzman Cabrera, Rafael
In this work a comparative theoretical analysis vs. experimental study on human blood under a magnetic field stimulation is presented. Twenty samples of leukoreduced human blood were stimulated alternant magnetic field using a Helmholtz coil system; this magnetic field induced an electromotive force in them. Theoretical calculations were performed for the induced electromotive force in a simple model of blood tissue under magnetic stimulation at frequencies: 50 Hz, 100 Hz, 800 Hz, and 1500 Hz. Experimental measurement was performed at the same frequencies for comparison purposes. Results show a high correlation between theoretical and experimental study, as well as effects of agglutination in the stimulated blood cells.
Multidetermination of thiamine HCl and pyridoxine HCl in their mixture using continuous daubechies and biorthogonal wavelet analysis
(Elsevier, 2003) Dinç, E.; Baleanu, Dumitru
A new graphical method based on the one-dimensional wavelet transform (WT) was proposed and tested on mixture of thiamine hydrochloride (THI) and pyridoxine hydrochloride (PYR) in the presence of strongly overlapping signals. We selected from the data of the UV-VIS absorption spectra a signal consisting of 1150 points corresponding to the concentration range 8-32 mg ml(-1) for each vitamin and we subjected it to Daubechies8 (DAUB8) and Biorthogonal6.8 (BIOR6.8) wavelet transforms. Since the peaks of the transformed signals were bigger than original ones a zero crossing method was applied to obtain the calibration graphs. In addition, the validity of Beer-Lambert law was assumed for the transformed signals. An appropriate scale setting was choosing to obtain an alternative calibration for each method. MATLAB 6.5 software was used for one-dimensional wavelet analysis and the basic concepts about wavelet method were given. The obtained results were successfully compared among each other as well as with those obtained by other literature methods. The method developed in this paper is rapid, easy to apply, not expensive and it is suitable for analyzing of the overlapping signals of compounds in their mixtures without any chemical pre-treatment. (C) 2002 Elsevier Science B.V. All rights reserved.
Citation - Scopus: 32
New extensions of Hermite–Hadamard inequalities via generalized proportional fractional integral
(John Wiley and Sons Inc, 2021) Mumcu, İlker; Set, Erhan; Akdemir, Ahmet Ocak; Jarad, Fahd
The main aim this work is to give Hermite–Hadamard inequalities for convex functions via generalized proportional fractional integrals. We also obtained extensions of Hermite–Hadamard type inequalities for generalized proportional fractional integrals. © 2021 Wiley Periodicals LLC
Citation - WoS: 13
Citation - Scopus: 17
Nonautonomous lump-periodic and analytical solutions tothe (3+1)-dimensional generalized Kadomtsev-Petviashviliequation
(Springer, 2023) Alquran, Marwan; Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, Dumitru
This work establishes the lump periodic and exact traveling wave solutions for the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation. We use the Hirota bilinear method, as well as the robust integration techniques tanh-coth expansion and rational sine-cosine, to provide such innovative solutions. In order to explain specific physical difficulties, innovative lump periodic and analytical solutions have been investigated. These discoveries have been proven to be useful in the transmission of long-wave and high-power communications networks. It is important to highlight that the results given in thiswork depict new features and reflect previously unknown physical dynamics for the governing model.
Citation - Scopus: 4
Nonlinear singular p-Laplacian boundary value problems in the frame of conformable derivative
(American Institute of Mathematical Sciences, 2021) Bouloudene, Mokhtar; Alqudah, Manar A.; Jarad, Fahd; Adjabi, Yassine; Abdeljawad, Thabet
This paper studies a class of fourth point singular boundary value problem of p-Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the order of the conformable differential equation and on the initial conditions. © 2021 American Institute of Mathematical Sciences. All rights reserved.
Numerical Simulation of Mixed Convection Squeezing Flow of a Hybrid Nanofluid Containing Magnetized Ferroparticles in 50%:50% of Ethylene Glycol–Water Mixture Base Fluids Between Two Disks With the Presence of a Non-linear Thermal Radiation Heat Flux
(Frontiers Media SA, 2020) Nisar, Kottakkaran Sooppy; Khan, Umair; Zaib, A.; Khan, Ilyas; Baleanu, Dumitru
Ferroliquids are an example of a colloidal suspension of magnetic nanomaterials and regular liquids. These fluids have numerous applications in medical science such as cell separation, targeting of drugs, magnetic resonance imaging, etc. The hybrid nanofluid is composed by scattering the magnetic nanomaterial of more than one type nanoparticles suspended into the base fluid. It has different scientific applications such as heat dissipation, dynamic sealing, damping, etc. Owing to the vast ferrofluid applications, the time-dependent squeezed flow of hybrid ferroliquids under the impact of non-linear radiation and mixed convection within two disks was explored for the first time in this analysis. Here, the cobalt and magnetite ferrofluids are considered and scattered in a 50%:50% mixture of water–EG (ethylene glycol). The similarity technique is used to reduce the leading PDEs into coupled non-linear ODEs. The transmuted equations together with recommended boundary restrictions are numerically solved via Matlab solver bvp4c. The opposing and assisting flows are considered. The impacts of an emerging parameter on fluid velocity and temperature field of hybrid ferroliquids are examined through the different graphical aids. The results showed that the opposite trend is scrutinized due to the magnetic influence on the temperature and velocity in the case of assisting and opposing flows. The velocity augments due to the volume fraction of nanoparticles in the assisting flow and declines in the opposing flow, while the opposite direction is noticed in the temperature field. © Copyright © 2020 Nisar, Khan, Zaib, Khan and Baleanu.
On a new class of fractional operators
(Springeropen, 2017) Jarad, Fahd; Uğurlu, Ekin; Abdeljawad, Thabet; Baleanu, Dumitru
This manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these operators.
On fractional order hybrid differential equations
(Hindawi Publishing Corporation, 2014) Herzallah, Mohamed A. E.; Baleanu, Dumitru
We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0 << 1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.
On hybrid contractions via simulation function in the context of quasi-metric spaces
(Yokohama Publications, 2021) Karapınar, Erdal; Fulga, Andreea
In this manuscript, we aim at investigating the existence of a fixed point theorem for the mappings that satisfy hybrid contraction in the setting of quasi-metric spaces. We provide examples to indicate the validity of the observed results.

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