Analytic solutions for a modified fractional three wave interaction equations with conformable derivative by unified method

Talafha, Adeeb G.; Alqaraleh, Sahar M.; Al‐Smadi, Mohammed; Hadid, Samir; Momani, Shaher

doi:10.1016/j.aej.2020.06.027

Cited by 15 publications

(5 citation statements)

References 47 publications

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“…The LSS of the system (11) is presented as: Taking inverse Laplace transform on both sides of system (14), to obtain the LRPS solution of the system (9), as…”

Section: Lrps Solution Of Tb Modelmentioning

confidence: 99%

“…Fractional derivatives have emerged as a powerful tool for modeling various real-life problems in biology, physics, control theory, and other engineering and scientific fields [7][8][9][10][11][12][13]. The utilization of numerical and approximate approaches has facilitated the computation of solutions for fractional differential equations (DEs) [14]. These fractional ordinary and partial differential equations (PDEs) play a pivotal role in diverse scientific and engineering disciplines [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Efficient Solutions with the LRPS Method for Non-Linear Fractional Order Tuberculosis Models

Alsulami,

Yasin,

Afzal

et al. 2024

Trends Sci

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In this research article, we present a novel Non-Linear Fractional Order Tuberculosis mathematical model (NLFOTB) and introduce an efficient technique to obtain its solution. Fractional Order Models (FOMs) have garnered significant attention in contemporary research due to their widespread applicability. We address the challenge of solving the coupled Initial Value Problems (IVPs) associated with NLFOTB models by utilizing the groundbreaking LRPS method, which combines the RPS approach with the Laplace transform operator. This innovative approach generates approximate solutions in rapidly converging series forms, offering enhanced efficiency and reduced computational effort compared to conventional methods. Through the implementation of the LRPS method, we successfully derive an approximate solution for the NLFOTB model, contributing significantly to the field. Furthermore, our proposed approach demonstrates its efficacy in accurately capturing the dynamics of Tuberculosis (TB) through extensive computations and graphical representations, contributing to a deeper understanding of TB dynamics within a mathematical framework. Additionally, the LRPS method shows promise in tackling real world problems involving differential equations of various orders. Future investigations can extend the application of the LRPS method to explore other Fractional Order Models, further validating its effectiveness in a wide range of epidemic scenarios. Consequently, our study not only provides valuable insights into Tuberculosis dynamics but also introduces a powerful computational tool applicable to various practical problems in diverse disciplines, making a substantial contribution to the field of mathematical modeling and computation. HIGHLIGHTS · The comprehensive study highlights the LRPS strategy’s efficiency and accuracy in approximating solutions for fractional order equations. The research demonstrates its capability to predict compartmental behavior accurately within the specified range · The discussions presented in the article significantly contribute to the field of epidemiology by introducing and showcasing the LRPS approach’s effectiveness. As a valuable tool for investigating and validating epidemic models, the LRPS method offers improved efficiency and convenience, thereby enhancing the understanding of disease dynamics · The researchers anticipate that their findings will inspire further exploration and utilization of the LRPS technique in solving nonlinear models. This, in turn, is expected to contribute to advancements in the broader field of epidemiology, fostering continued innovation and development GRAPHICAL ABSTRACT

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“…The LSS of the system (11) is presented as: Taking inverse Laplace transform on both sides of system (14), to obtain the LRPS solution of the system (9), as…”

Section: Lrps Solution Of Tb Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Efficient Solutions with the LRPS Method for Non-Linear Fractional Order Tuberculosis Models

Alsulami,

Yasin,

Afzal

et al. 2024

Trends Sci

View full text Add to dashboard Cite

show abstract

“…A particular group of non-local field theories plays an outstanding role and may be described with operators of fractional nature and is specified within the framework of fractional calculus. 4–9…”

Section: Background Of Fractional Calculusmentioning

confidence: 99%

“…In addition, the subject of fractional derivatives can be widely applied in many real life applications, such as; engineering, mathematical biology, quantum physics, fluid mechanics fields. 6–11 Due to the fast development of software programs such as Mat Lab, Mathematica and Maple, many new powerful analytical techniques have been proposed to find new and approximate solutions for fractional linear and nonlinear differential equations such as; the sub-equation method, 12 Exponential function method, 13 first integral method, 14 the expansion method, 15 fractional reproducing kernel method, 16–18 fractional Adomian decomposition method, 19 fractional homotopy perturbation, 20 fractional homotopy analysis, 21 fractional residual power series, 22–25 fractional Laplace decomposition, 26 fractional differential transform method 27–30 and other advanced numerical methods. 31–34…”

Section: Introductionmentioning

confidence: 99%

An efficient technique to solve coupled–time fractional Boussinesq–Burger equation using fractional decomposition method

Rawashdeh

Bani-Issa

2021

Advances in Mechanical Engineering

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For this work, a novel numerical approach is proposed to obtain solution for the class of coupled time-fractional Boussinesq–Burger equations which is a nonlinear system. This system under consideration is endowed with Caputo time-fractional derivative. By means of the natural decomposition approach, approximate solutions of the proposed nonlinear fractional system are obtained where the exact solutions are presented in the classical case of fractional order at [Formula: see text]. Some numerical examples are given to support the theoretical framework and to point out the role and the effectiveness of the intended method. Our results clearly show the approximate analytical solutions eventually will converge quickly to the already known exact solutions. AMS Classification: 35A22, 35C05, 35C10, 35R11, 44A30.

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“…With the development of research, there are many publications studying the existence, stability, controllability, and periodicity of solutions for non-instantaneous impulsive differential equations; see for example [1,5,7,9,11,14,15,16,18,20,22,23,24,25]. Motivated by the results based on conformable derivatives, [2,3,4,6,8,10,13,17,19,21], we consider the homogeneous linear conformable non-autonomous problem…”

Section: Introductionmentioning

confidence: 99%

Properties of the solutions to periodic conformable non-autonomous non-instantaneous impulsive differential equations

Ding,

Liu

2024

ejde

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In this article, we study properties of the solutions to periodic non-autonomous conformable non-instantaneous impulsive differential equations. We use a conformable Cauchy matrix and obtain some basic properties of the periodic solution to the homogeneous and non=homogeneous problems. We consider the periodicity of solutions to nonlinear problem via a fixed theorem. For more information see https://ejde.math.txstate.edu/Volumes/2024/30/abstr.html

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Analytic solutions for a modified fractional three wave interaction equations with conformable derivative by unified method

Cited by 15 publications

References 47 publications

Efficient Solutions with the LRPS Method for Non-Linear Fractional Order Tuberculosis Models

Efficient Solutions with the LRPS Method for Non-Linear Fractional Order Tuberculosis Models

An efficient technique to solve coupled–time fractional Boussinesq–Burger equation using fractional decomposition method

Properties of the solutions to periodic conformable non-autonomous non-instantaneous impulsive differential equations

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