Conformable Double Laplace–Sumudu Iterative Method

Ahmed, Shams A.; Qazza, Ahmad; Saadeh, Rania; Elzaki, Tarig M.

doi:10.3390/sym15010078

Cited by 8 publications

(6 citation statements)

References 28 publications

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“…Khalil et al [4] developed the conformable derivative (CD), a more recent development of the conventional limit definition for the derivative of a function. This new derivative has been used with other methods [10][11][12][13] in a lot of different situations because it is so simple to use. Hashemi [10] established the invariant subspace approach for obtaining accurate solutions to a variety of conformable time fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…Osman et al [11] came up with a new way to solve singular fractional pseudohyperbolic and pseudoparabolic equations using a modified double conformable Laplace transform. A lot of NPDEs with conformable derivatives were solved using the conformable double Laplace-Sumudu iterative approach [12]. Bhanotar and Kaabar [13] came up with the conformable triple Laplace transform decomposition technique to solve NFPDEs analytically.…”

Section: Introductionmentioning

confidence: 99%

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An Efficient New Technique for Solving Nonlinear Problems Involving the Conformable Fractional Derivatives

Ahmed

2024

Journal of Applied Mathematics

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In this paper, an efficient new technique is used for solving nonlinear fractional problems that satisfy specific criteria. This technique is referred to as the double conformable fractional Laplace-Elzaki decomposition method (DCFLEDM). This approach combines the double Laplace-Elzaki transform method with the Adomian decomposition method. The fundamental concepts and findings of the recently suggested transformation are presented. For the purpose of assessing the accuracy of our approach, we provide three examples and introduce the series solutions of these equations using DCLEDM. The results show that the proposed strategy is a very effective, reliable, and efficient approach for addressing nonlinear fractional problems using the conformable derivative.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Efficient New Technique for Solving Nonlinear Problems Involving the Conformable Fractional Derivatives

Ahmed

2024

Journal of Applied Mathematics

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“…is presented for the first time to solve these equations. The proposed method shows its simplicity and applicability to solve problems in physical chemistry [9,15]. The utilization of the Mohanad transform (M.T) in solving a chemical application, specifically in determining chemical reactant concentrations within a series reaction, can be attributed to several reasons: Complexity of Chemical Reactions: Chemical reactions, especially in series, can involve intricate kinetics and complex equations describing the change in concentrations over time.…”

Section: Introductionmentioning

confidence: 99%

The Mohanad Transforms and Their Applications for Solving Systems of Differential Equations

Saadeh,

Alshawabkeh,

Khalil

et al. 2024

Eur. J. Pure Appl. Math.

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In recent years, Mohanad transform, a mathematical approach, has drawn a lot of interest from researchers. It is useful for solving many engineering and scientific problems, such as those involving electric circuits, population growth, vibrational beams, and heat conduction. The Mohanad transform is defined and introduced in this study, along with its fundamental qualities,including linearity and convolution. It is also discussed in connection with other integral transforms and how it is used in derivatives. Additionally, we use the Mohanad transform to solve a few systems of ordinary differential equations (ODEs) and review its properties in this paper. Determining the concentration of a chemical reactant (material) in a series is a physical chemistry problem that we use in the application part. We achieve this by developing a model based on ordinary differential equations (ODEs) and then solving them using the Mohanad transform. This research proves that, with little computational effort, we can get the exact solutions of ordinary differential equations (ODEs) via the Mohanad transform. We used graphs and tables to show our answer.

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“…Examples include a smooth transition from wave propagation to diffusion or from local to nonlocal dynamics [6–8]. There are several methods that are developed in literature to solve fractional differential equations, such as homotopy analysis method [9], Laplace residual power series [10], iterative method [11], and integral transforms [12].…”

Section: Introductionmentioning

confidence: 99%

A study of double general transform for solving fractional partial differential equations

Saadeh

Ghazal

Burqan

2023

Math Methods in App Sciences

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In this research, we introduce the basic properties of the single and double general transforms. New interesting results related to fractional operators in the sense of Caputo derivative are investigated and proved. In this study, the general double transformation is utilized to study the application on some special functions, such as the Mittag–Leffler function, and on the Caputo's fractional derivative of different and higher orders. Moreover, we establish new interesting formulas and prove some theories that can save efforts and time for researchers as they investigate the properties and applications of integral transformations on fractional operators. The results obtained in this research are tested by solving different types of fractional partial differential equations to obtain exact solutions. The outcomes of this article are valuable to researchers and mathematicians who are interested in the solving fractional partial differential equations via integral transforms, which are considered as important techniques to handle these equations.

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Conformable Double Laplace–Sumudu Iterative Method

Cited by 8 publications

References 28 publications

An Efficient New Technique for Solving Nonlinear Problems Involving the Conformable Fractional Derivatives

An Efficient New Technique for Solving Nonlinear Problems Involving the Conformable Fractional Derivatives

The Mohanad Transforms and Their Applications for Solving Systems of Differential Equations

A study of double general transform for solving fractional partial differential equations

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