Browsing by Author "Baleanu, D."

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Citation Count: Heydari, M. H.; Hosseininia, M.; Baleanu, D. (2023). "A Computational Approach Based On The Fractional Euler Functions And Chebyshev Cardinal Functions For Distributed-Order Time Fractional 2D Diffusion Equation", Alexandrıa Engineering Journal, Vol. 67, pp. 643-653.
A Computational Approach Based On The Fractional Euler Functions And Chebyshev Cardinal Functions For Distributed-Order Time Fractional 2D Diffusion Equation
(Alexandrıa Engineering Journal, 2023) Heydari, M. H.; Hosseininia, M.; Baleanu, D.; 56389
In this paper, the distributed-order time fractional diffusion equation is introduced and studied. The Caputo fractional derivative is utilized to define this distributed-order fractional derivative. A hybrid approach based on the fractional Euler functions and 2D Chebyshev cardinal functions is proposed to derive a numerical solution for the problem under consideration. It should be noted that the Chebyshev cardinal functions process many useful properties, such as orthogonal-ity, cardinality and spectral accuracy. To construct the hybrid method, fractional derivative oper-ational matrix of the fractional Euler functions and partial derivatives operational matrices of the 2D Chebyshev cardinal functions are obtained. Using the obtained operational matrices and the Gauss-Legendre quadrature formula as well as the collocation approach, an algebraic system of equations is derived instead of the main problem that can be solved easily. The accuracy of the approach is tested numerically by solving three examples. The reported results confirm that the established hybrid scheme is highly accurate in providing acceptable results
Citation Count: Dehingia, Kaushik...et.al. (2022). "A Detailed Study on a Tumor Model with Delayed Growth of Pro-Tumor Macrophages", International Journal of Applied and Computational Mathematics, Vol.8, No.5
A Detailed Study on a Tumor Model with Delayed Growth of Pro-Tumor Macrophages
(2022) Dehingia, Kaushik; Hosseini, Kamyar; Salahshour, Soheil; Baleanu, D.; 56389
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 under certain conditions, and the stability of the interior steady-state is affected by the discrete-time delay; as a result, the unstable system experiences a Hopf bifurcation and gets stabilized. Furthermore, the transversality conditions for the existence of Hopf bifurcations are derived. Several graphical representations in two and three-dimensional postures are given to examine the validity of the results provided in the current study.
Citation Count: Hosseini, K.;...et.al. "A new generalized KdV equation: Its lump-type, complexiton and soliton solutions", International Journal of Modern Physics B, Vol.36, No.31.
A new generalized KdV equation: Its lump-type, complexiton and soliton solutions
(2022) Hosseini, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; Dehingia, K.; 56389
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 are categorized as lump-type, complexiton, and soliton solutions. To exhibit the physical mechanism of the obtained solutions, several graphical illustrations are given for particular choices of the involved parameters. As a direct consequence, diverse wave structures given in this paper enrich the studies on the KdV-type equations.
Citation Count: Heydari, M. H.; Razzaghi, M.; Baleanu, D. (2023). "A numerical method based on the piecewise Jacobi functions for distributed-order fractional Schrodinger equation", Communications In Nonlinear Science And Numerical Simulation, Vol.116.
A numerical method based on the piecewise Jacobi functions for distributed-order fractional Schrodinger equation
(Communications In Nonlinear Science And Numerical Simulation, 2023) Heydari, M. H.; Razzaghi, M.; Baleanu, D.; 56389
In this work, the distributed-order time fractional version of the Schrodinger 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 novel family of basis functions are defined. A new formulation for the Caputo fractional derivative of these functions is derived. A numerical method based upon these piecewise functions together with the classical Jacobi polynomials and the Gauss- Legendre quadrature rule is constructed to solve the introduced problem. This method converts the mentioned problem into an algebraic problem that can easily be solved. The accuracy of the method is examined numerically by solving some examples.
Citation Count: Habenom, Haile;...et.al. (2021). "A Numerical Simulation on the Effect of Vaccination and Treatments for the Fractional Hepatitis B Model", Journal Of Computational And Nonlinear Dynamics, Vol.16, No.1.
A Numerical Simulation on the Effect of Vaccination and Treatments for the Fractional Hepatitis B Model
(2021) Habenom, Haile; Suthar, D. L.; Baleanu, D.; Purohit, S. D.; 56389
The aim of this paper is to develop a fractional order mathematical model for describing the spread of hepatitis B virus (HBV). We also provide a rigorous mathematical analysis of the stability of the disease-free equilibrium (DFE) and the endemic equilibrium of the system based on the basic reproduction number. Here, the infectious disease HBV model is described mathematically in a nonlinear system of differential equations in a caputo sense, and hence, Jacobi collocation method is used to reduce into a system of nonlinear equations. Finally, Newton Raphson method is used for the systems of nonlinear equations to arrive at an approximate solution and matlab 2018 has helped us to simulate the nature of each compartment and effects of the possible control strategies (i.e., vaccination and isolation).
Citation Count: Soori, Z.; Aminataei, A.; Baleanu, D. (2023). "A Reduced-Order Finite Difference Scheme Based on POD for Fractional Stochastic Advection-Diffusion Equation", Iranian Journal Of Science, Vol.47, No.4, pp.1299-1311.
A Reduced-Order Finite Difference Scheme Based on POD for Fractional Stochastic Advection-Diffusion Equation
(2023) Soori, Z.; Aminataei, A.; Baleanu, D.; 56389
This article introduces a new scheme for the fractional stochastic advection–diffusion equation (FSA-DE) in time where the fractional term is expressed in Caputo sence of order a ð0\a\1Þ. First, an L1 approximation is employed to estimate the Caputo derivative. Then, the spatial derivative is approximated by a second-order finite difference scheme. Moreover, we combine the implicit finite difference (IFD) scheme with the proper orthogonal decomposition (POD) method to reduce the used CPU time. In other words, the POD based reduced-order IFD scheme is obtained. The proposed scheme can be regarded as the modification of the exiting work (Mirzaee et al. in J Sci Technol Trans Sci 45:607–617, 2001). The numerical results are provided to confirm the feasibility and efficiency of the proposed method.
Citation Count: Pandey, Amit K.;...et.al. (2022). "An efficient algorithm for the numerical evaluation of pseudo differential operator with error estimation", AIMS Mathematics, Vol.7, No.10, pp.17829-17842.
An efficient algorithm for the numerical evaluation of pseudo differential operator with error estimation
(2022) Pandey, Amit K.; Tripathi, Manoj P.; Singh, Harendra; Rao, Pentyala S.; Kumar, Devendra; Baleanu, D.; 56389
In this paper we introduce an efficient and new numerical algorithm for evaluating a pseudo differential operator. The proposed algorithm is time saving and fruitful. The theoretical as well as numerical error estimation of the algorithm is established, together with its stability analysis. We have provided numerical illustrations and established that the numerical findings echo the analytical findings. The proposed technique has a convergence rate of order three. CPU time of computation is also listed. Trueness of numerical findings are validated using figures.
Citation Count: Heydari, M.H.; Hosseininia, M.; Baleanu, D. (2023). "An efficient method for 3D Helmholtz equation with complex solution", AIMS Mathematics, Vol8, No.6, pp. 14792-14819.
An efficient method for 3D Helmholtz equation with complex solution
(2023) Heydari, M.H.; Hosseininia, M.; Baleanu, D.; 56389
The Helmholtz equation as an elliptic partial differential equation possesses many applications in the time-harmonic wave propagation phenomena, such as the acoustic cavity and radiation wave. In this paper, we establish a numerical method based on the orthonormal shifted discrete Chebyshev polynomials for finding complex solution of this equation. The presented method transforms the Helmholtz equation into an algebraic system of equations that can be easily solved. Four practical examples are examined to show the accuracy of the proposed technique.
Citation Count: Abdelhakem M.;...et.al. (2023). "Approximating system of ordinary differential-algebraic equations via derivative of Legendre polynomials operational matrices", International Journal of Modern Physics C, Vol.34, No.3.
Approximating system of ordinary differential-algebraic equations via derivative of Legendre polynomials operational matrices
(2023) Abdelhakem, M.; Baleanu, D.; Agarwal, P.; Moussa, H.; 56389
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 di®erential-algebraic equations. An algorithm via those matrices has been designed. The accuracy and e±ciency of the proposed algorithm had been shown by two techniques, theoretically, via the boundedness of the approximated expansion and numerically through numerical examples.
Citation Count: Hosseini K.;...et.al. (2023). "Bäcklund Transformation, Complexiton, and Solitons of a (4 + 1)-dimensional Nonlinear Evolutionary Equation", International Journal of Applied and Computational Mathematics, Vol.8, No.6.
Bäcklund Transformation, Complexiton, and Solitons of a (4 + 1)-dimensional Nonlinear Evolutionary Equation
(2022) Hosseini, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; 56389
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 then employed to acquire the solitons of the governing model. In the end, the complexiton of the 4D-NLE equation is retrieved using the Zhou–Ma method. As the completion of studies, several graphical representations are considered for different parameter values to show the dynamics of complexiton and solitons.
Citation Count: Karthikeyan, P.; Karthikeyan, K.; Baleanu, D. (2023). "Compactness Results on Integro-Differential Equations InvolvingΨ-Hilfer Fractional Derivative", Discontinuity, Nonlinearity, and Complexity, Vol.12, No.3, pp.631-642.
Compactness Results on Integro-Differential Equations InvolvingΨ-Hilfer Fractional Derivative
(2023) Karthikeyan, P.; Karthikeyan, K.; Baleanu, D.; 56389
We analyze the existence results of fractional integro-differential equations via Ψ-Hilfer fractional derivative with nonlocal multi-point condition by using Schauder fixed point theorem. To establish the sufficient conditions for compactness of operators and an example is also discussed.
Citation Count: Correa-Escudero, I.L.;...et.al. (2022). "Correcting dimensional mismatch in fractional models with power, exponential and proportional kernel: Application to electrical systems", Results in Physics, Vol.40.
Correcting dimensional mismatch in fractional models with power, exponential and proportional kernel: Application to electrical systems
(2022) Correa-Escudero, I.L.; Gómez-Aguilar, J.F.; López-López, M.G.; Alvarado-Martínez, V.M.; Baleanu, D.; 56389
Fractional calculus is a powerful tool for describing diffusion phenomena, anomalous behaviors, and in general, systems with highly complex dynamics. However, the application of fractional operators for modeling purposes, produces a dimensional problem. In this paper, the fractional models of the RC, RL, RLC electrical circuits, a supercapacitor, a bank of supercapacitors, a LiFePO4 battery and a direct current motor are presented. A correction parameter is included in their formulation in order to preserve dimensionality in the physical equations. The optimal value of this parameter was determined via particle swarm optimization algorithm using numerical simulations and experimental data. Thus, a direct and effective approach for the construction of dimensionally corrected fractional models with power, exponential-decay and constant proportional Caputo hybrid derivative is presented. To show the effectiveness of the procedure, the time-response of the models is compared with experimental data and the modeling error is computed. The numerical solutions of the models were obtained using a numerical method based on the Adams methods.
Citation Count: Baleanu, D...et.al. "Dynamical behaviours and stability analysis of a generalized fractional model with a real case study", Journal of Advanced Research, Vol.48, pp.157-173.
Dynamical behaviours and stability analysis of a generalized fractional model with a real case study
(2023) Baleanu, D.; Arshad, S.; Jajarmi, A.; Shokat, W.; Ghassabzade, F. Akhavan; Wali, M.; 56389
Introduction: Mathematical modelling is a rapidly expanding field that offers new and interesting opportunities for both mathematicians and biologists. Concerning COVID-19, this powerful tool may help humans to prevent the spread of this disease, which has affected the livelihood of all people badly. Objectives: The main objective of this research is to explore an efficient mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. Methods: The new model in this paper is formulated in the Caputo sense, employs a nonlinear time-varying transmission rate, and consists of ten population classes including susceptible, infected, diagnosed, ailing, recognized, infected real, threatened, diagnosed recovered, healed, and extinct people. The existence of a unique solution is explored for the new model, and the associated dynamical behaviours are discussed in terms of equilibrium points, invariant region, local and global stability, and basic reproduction number. To implement the proposed model numerically, an efficient approximation scheme is employed by the combination of Laplace transform and a successive substitution approach; besides, the corresponding convergence analysis is also investigated. Results: Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic in Italy. By using these comparisons between the simulated and measured data, we find the best value of the fractional order with minimum absolute and relative errors. Also, the impact of different parameters on the spread of viral infection is analyzed and studied. Conclusion: According to the comparative results with real data, we justify the use of fractional concepts in the mathematical modelling, for the new non-integer formalism simulates the reality more precisely than the classical framework.
Citation Count: Madhukalya B...et.al. "Effect of ion and negative ion temperatures on KdV and mKdV solitons in a multicomponent plasma", Nonlinear Dynamics, Vol.111, No.9, pp.8659-8671.
Effect of ion and negative ion temperatures on KdV and mKdV solitons in a multicomponent plasma
(2023) Madhukalya, B.; Das, R.; Hosseini, K.; Baleanu, D.; Hıncal, E.; 56389
The formation of ion-acoustic solitons (IASs) in an unmagnetized plasma with negative ions has been investigated through the KdV equation in both the situations Q′(=mj/mi=negativetopositiveionmassratio) less and greater than one and the mKdV equation only for Q′> 1. The existence of both KdV and mKdV solitons has been established for α(=iontoelectrontemperatureratio)>β(=negativeiontoelectrontemperatureratio) and α< β, which is the new outcome of the current investigation. Furthermore, the existence of both compressive and rarefactive solitons for Q′> 1 and Q′< 1 has been demonstrated.
Citation Count: Khoshkenar, A. (2022). "Further studies on ordinary differential equations involving the M-fractional derivative", AIMS Mathematics, Vol.7, No.6, pp.10977-10993.
Further studies on ordinary differential equations involving the M-fractional derivative
(2022) Khoshkenar, A.; Ilie, M.; Hosseini, K.; Baleanu, D.; Salahshour, S.; Park, C.; Lee, J.R.; 56389
In the current paper, the power series based on the M-fractional derivative is formally introduced. More peciesely, the Taylor and Maclaurin expansions are generalized for fractional-order differentiable functions in accordance with the M-fractional derivative. Some new definitions, theorems, and corollaries regarding the power series in the M sense are presented and formally proved. Several ordinary differential equations (ODEs) involving the M-fractional derivative are solved to examine the validity of the results presented in the current study.
Citation Count: Ziane D.;...et.al. (2019). "Local fractional Sumudu decomposition method for linear partial differential equations with local fractional derivative", Journal of King Saud University - Science, Vol.31, No.1, pp.83-88.
Local fractional Sumudu decomposition method for linear partial differential equations with local fractional derivative
(2019) Ziane, D.; Baleanu, D.; Belghaba, K.; Hamdi Cherif, M.; 56389
In the paper, a combined form of the Sumudu transform method with the Adomian decomposition method in the sense of local fractional derivative, is proposed to solve fractional partial differential equations. This method is called the local fractional Sumudu decomposition method (LFSDM) and is used to describe the non-differentiable problems. It would be interesting to apply LFSDM to some well-known problems to see the benefits obtained.
Citation Count: Koundal, Reena;...et.al. (2021). "Lucas Wavelet Scheme for Fractional Bagley–Torvik Equations: Gauss–Jacobi Approach", International Journal of Applied and Computational Mathematics, Vol.8, No.1.
Lucas Wavelet Scheme for Fractional Bagley–Torvik Equations: Gauss–Jacobi Approach
(2022) Koundal, Reena; Kumar, Rakesh; Srivastava, K.; Baleanu, D.; 56389
A novel technique called as Lucas wavelet scheme (LWS) is prepared for the treatment of Bagley–Torvik equations (BTEs). Lucas wavelets for the approximation of unknown functions appearing in BTEs are introduced. Fractional derivatives are evaluated by employing Gauss–Jacobi quadrature formula. Further, well-known least square method (LSM) is adopted to compute the residual function, and the system of algebraic equation is obtained. Convergence criterion is derived and error bounds are obtained for the established technique. The scheme is investigated by choosing some reliable test problems through tables and figures, which ensures the convenience, validity and applicability of LWS.
Citation Count: Abdelhakem M.;...et.al. (2022). "Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems", Computational and Applied Mathematics, Vol.41,No.6.
Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems
(2022) Abdelhakem, M.; Ahmed, A.; Baleanu, D.; El-Kady, M.; 56389
We introduce new differentiation matrices based on the pseudospectral collocation method. Monic Chebyshev polynomials (MCPs) were used as trial functions in differentiation matrices (D-matrices). Those matrices have been used to approximate the solutions of higher-order ordinary differential equations (H-ODEs). Two techniques will be used in this work. The first technique is a direct approximation of the H-ODE. While the second technique depends on transforming the H-ODE into a system of lower order ODEs. We discuss the error analysis of these D-matrices in-depth. Also, the approximation and truncation error convergence have been presented to improve the error analysis. Some numerical test fun
Citation Count: Hosseini K.,...et.al. (2022). "Multi-complexiton and positive multi-complexiton structures to a generalized B-type Kadomtsev−Petviashvili equation", Journal of Ocean Engineering and Science.
Multi-complexiton and positive multi-complexiton structures to a generalized B-type Kadomtsev−Petviashvili equation
(2022) Hosseini, K.; Baleanu, D.; Rezapour, S.; Salahshour, S.; Mirzazadeh, M.; Samavat, M.; 56389
Recently, Zhang et al. (International Journal of Modern Physics B 30 (2016) 1640029) constructed N-wave solutions of a generalized B-type Kadomtsev−Petviashvili (gbKP) equation using the linear superposition method. The authors’ aim of the present paper is to derive multi-complexiton and positive multi-complexiton structures of the gbKP equation through considering N-wave solutions and applying specific systematic methods. To investigate the dynamical characteristics of positive multi-complexiton structures, particularly single and double positive complexitons, several two and three-dimensional simulations are formally considered. The results of the current research enrich the studies regarding the gbKP equation.
Citation Count: Nigmatullin, R. R.; Ionescu, C.; Baleanu, D. (2014). "NIMRAD: novel technique for respiratory data treatment", SIGNAL IMAGE AND VIDEO PROCESSING, Vol. 8., No. 8., pp. 1517-1532.
NIMRAD: novel technique for respiratory data treatment
(2014) Nigmatullin, R. R.; Ionescu, C.; Baleanu, D.; 56389
This paper illustrates the efficiency and simplicity of a new technique which is determined in this paper as NIMRAD (the non-invasive methods of the reduced analysis of data) for describing information extracted from biological signals. As a specific example, we consider the respiratory data. The NIMRAD can be applied for quantitative description of data recorded for complex systems in cases where the adequate model is absent and the treatment procedure should not contain any uncontrollable error. The theoretical developments are applied to signals measured from the respiratory system by means of the forced oscillation technique based on non-invasive lung function test. In order to verify the feasibility of the proposed algorithm for developing new diagnosis tools, we apply NIMRAD on two different respiratory data sets, namely from a healthy subject and from a patient diagnosed with asthma. The results are promising and suggest that NIMRAD could be further tailored and used for specific clinical applications.