A New Approach to (3+1) Dimensional Boiti–Leon–Manna–Pempinelli Equation

Yel, Gülnur; Aktürk, Tolga

doi:10.2478/amns.2020.1.00029

Cited by 22 publications

(10 citation statements)

References 36 publications

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“…The matrix reflects the user's rating of the item. The recommendation relation is shown in formula (10).…”

Section: Contextual Interest Modelingmentioning

confidence: 99%

“…The experimental evaluation criteria in this paper mainly include two aspects: First, we test whether the parallel mining of big data based on Hadoop can improve the performance of the model calculation. The second is to test situational recommendation mitigation to reduce recommendation accuracy caused by data sparsity [10]. The speedup ratio is mainly used to compare the time it takes for a specific algorithm to run in two different environments, singlemachine, and parallel computing.…”

Section: Dataset and Evaluation Criteriamentioning

confidence: 99%

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University Library Lending System Model Based on Fractional Differential Equations

Liu

Hatamleh

2022

Applied Mathematics and Nonlinear Sciences

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How to find books suitable for them from the massive book information is a problem that needs to be considered at present for university library users. This paper proposes a personalized recommendation system for digital libraries utilizing fractional differential equations. At the same time, we use the idea of a collaborative filtering algorithm to recommend books for new users. Finally, we use the accurate data of the library to design a personalized book recommendation system for university libraries. The research shows that the university library lending system based on fractional differential equations has improved user experience.

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“…The matrix reflects the user's rating of the item. The recommendation relation is shown in formula (10).…”

Section: Contextual Interest Modelingmentioning

confidence: 99%

Section: Dataset and Evaluation Criteriamentioning

confidence: 99%

University Library Lending System Model Based on Fractional Differential Equations

Liu

Hatamleh

2022

Applied Mathematics and Nonlinear Sciences

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“…Cordero et al have observed the stability analysis of the fourth-order iterative method in [16]. The (3 +1) Dimensional Boiti-Leon-Manna-Pempinelli equation has been deeply studied in [17]. Using time scale calculus, discrete normal vector field approximation has been presented in [18].…”

Section: Introductionmentioning

confidence: 99%

“…Classical Boussinesq equations have been immensely studied in [20]. Traveling wave solutions of nonlinear Klein Gordon equation were observed in [21] and so on [15,17,18,.…”

Section: Introductionmentioning

confidence: 99%

Regarding New Traveling Wave Solutions for the Mathematical Model Arising in Telecommunications

Baskonus

Guirao

Kumar³

et al. 2021

Advances in Mathematical Physics

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This research paper focuses on the application of the tanh function method to find the soliton solutions of the (2+1)-dimensional nonlinear electrical transmission line model. Materials used to form a transmitting line are very important to transmit electric charge. In this sense, we find some new voltage behaviors such as dark, trigonometric, and complex function solutions. Choosing some suitable values of parameters, we present some various surfaces of results obtained in this paper. These results play an important role in telecommunications lines used to stand for wave propagations.

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“…There are many robust, stable, and effective methods that have been developed for constructing exact, approximate analytical and numerical solutions for NPDEs. Particularly, the methods have been extensively used to find exact solutions for NPDEs, such as the (G /G, 1/G)-expansion method [1], the modified G /G 2 -expansion method [2], the Jacobi elliptic equation method [3], the sine-Gordon expansion method [4,5], the extended direct algebraic method [6,7], the modified Exp-function method [8,9], and the Kudryashov method [10,11]. However, the focus of this work is to search for exact solutions of certain nonlinear partial integro-differential equations (PIDEs) converted into NPDEs in some ways.…”

Section: Introductionmentioning

confidence: 99%

Application of the Exp-Function and Generalized Kudryashov Methods for Obtaining New Exact Solutions of Certain Nonlinear Conformable Time Partial Integro-Differential Equations

2021

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The key objective of this paper is to construct exact traveling wave solutions of the conformable time second integro-differential Kadomtsev–Petviashvili (KP) hierarchy equation using the Exp-function method and the (2 + 1)-dimensional conformable time partial integro-differential Jaulent–Miodek (JM) evolution equation utilizing the generalized Kudryashov method. These two problems involve the conformable partial derivative with respect to time. Initially, the conformable time partial integro-differential equations can be converted into nonlinear ordinary differential equations via a fractional complex transformation. The resulting equations are then analytically solved via the corresponding methods. As a result, the explicit exact solutions for these two equations can be expressed in terms of exponential functions. Setting some specific parameter values and varying values of the fractional order in the equations, their 3D, 2D, and contour solutions are graphically shown and physically characterized as, for instance, a bell-shaped solitary wave solution, a kink-type solution, and a singular multiple-soliton solution. To the best of the authors’ knowledge, the results of the equations obtained using the proposed methods are novel and reported here for the first time. The methods are simple, very powerful, and reliable for solving other nonlinear conformable time partial integro-differential equations arising in many applications.

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A New Approach to (3+1) Dimensional Boiti–Leon–Manna–Pempinelli Equation

Cited by 22 publications

References 36 publications

University Library Lending System Model Based on Fractional Differential Equations

University Library Lending System Model Based on Fractional Differential Equations

Regarding New Traveling Wave Solutions for the Mathematical Model Arising in Telecommunications

Application of the Exp-Function and Generalized Kudryashov Methods for Obtaining New Exact Solutions of Certain Nonlinear Conformable Time Partial Integro-Differential Equations

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