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On Time Fractional Partial Differential Equations and Their Solution by Certain Formable Transform Decomposition Method

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Computer Modeling in Engineering & Sciences 2023年第9期136卷 3121-3139页

作者： Rania Saadeh ahmad qazza Aliaa Burqan Shrideh Al-Omari Department of Mathematics Zarqa UniversityZarqa13110Jordan Department of Mathematics Faculty of ScienceAl-Balqa Applied UniversityAmman11134Jordan

This paper aims to investigate a new efficient method for solving time fractional partial differential *** this orientation,a reliable formable transform decomposition method has been designed and developed,which is a novel combination of the formable integral transform and the decomposition ***,certain accurate solutions for time-fractional partial differential equations have been *** under concern demandsmore simple calculations and fewer efforts compared to the ***,the posed formable transformdecompositionmethod has been utilized to yield a series solution for given fractional partial differential ***,several interesting formulas relevant to the formable integral transform are applied to fractional operators which are performed as an excellent application to the existing ***,the formable transform decomposition method has been employed for finding a series solution to a time-fractional Klein-Gordon *** and above,some numerical simulations are also provided to ensure reliability and accuracy of the new approach.

关键词： Caputo derivative fractional differential equations formable transform time-fractional klein-gordon equation decomposition method

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Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

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Computer Modeling in Engineering & Sciences 2024年第2期138卷 1593-1616页

作者： Rania Saadah Mohammed Amleh ahmad qazza Shrideh Al-Omari Ahmet Ocak Akdemir Department of Mathematics Faculty of ScienceZarqa UniversityZarqa13110Jordan Department of Mathematics Faculty of ScienceAl-Balqa Applied UniversityAmman11134Jordan Department of Mathematics Faculty of Science and LettersAgri Ibrahim莈鏴n UniversityAgri04100Turkey

In this study,we aimto investigate certain triple integral transformand its application to a class of partial *** discuss various properties of the new transformincluding inversion, linearity, existence, scaling andshifting, etc. Then,we derive several results enfolding partial derivatives and establish amulti-convolution ***, we apply the aforementioned transform to some classical functions and many types of partial differentialequations involving heat equations,wave equations, Laplace equations, and Poisson equations ***,wedraw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving differentvalues in their variables.

关键词： ARA transform double ARA transform triple ARA transform partial differential equations integral transform

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Composite Fractional Trapezoidal Rule with Romberg Integration

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Computer Modeling in Engineering & Sciences 2024年第9期140卷 2729-2745页

作者： Iqbal M.Batiha Rania Saadeh Iqbal H.Jebril ahmad qazza Abeer A.Al-Nana Shaher Momani Department of Mathematics Al Zaytoonah University of JordanAmman11733Jordan Nonlinear Dynamics Research Center(NDRC) Ajman UniversityAjman 346United Arab Emirates Department of Mathematics Faculty of ScienceZarqa UniversityZarqa13110Jordan Department of Mathematics Prince Sattam Bin Abdulaziz UniversityAlkharj11942Saudi Arabia Department of Mathematics The University of JordanAmman11942Jordan

The aim of this research is to demonstrate a novel scheme for approximating the Riemann-Liouville fractional integral *** would be achieved by first establishing a fractional-order version of the 2-point Trapezoidal rule and then by proposing another fractional-order version of the(n+1)-composite Trapezoidal *** particular,the so-called divided-difference formula is typically employed to derive the 2-point Trapezoidal rule,which has accordingly been used to derive a more accurate fractional-order formula called the(n+1)-composite Trapezoidal ***,in order to increase the accuracy of the proposed approximations by reducing the true errors,we incorporate the so-called Romberg integration,which is an extrapolation formula of the Trapezoidal rule for integration,into our proposed *** numerical examples are provided and compared with a modern definition of the Riemann-Liouville fractional integral operator to illustrate the efficacy of our scheme.

关键词： Composite fractional Trapezoidal rule Romberg integration

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