New Implementation of Residual Power Series for Solving Fuzzy Fractional Riccati Equation

Alshorman, Moath Ali; Zamri, Nurnadiah; Ali, Mohammed; Albzeirat, Asia Khalaf

doi:10.32732/jmo.2018.10.2.81

Cited by 3 publications

(1 citation statement)

References 26 publications

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“…This technique needs less computational requirements with high precision as well as less time. Recently, very few researchers have studied the solution of fuzzy DE using the RPSM [18–21].…”

Section: Introductionmentioning

confidence: 99%

Analysis of time‐fractional fuzzy vibration equation of large membranes using double parametric based Residual power series method

Jena

Sedighi

2020

Z Angew Math Mech

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The study of the time‐fractional vibration equation (VE) of large membranes is vital due to its widespread applications. Various researchers have investigated the titled problem in which the variables and parameters have been considered as crisp/exact. However, in actual practice, this may contain uncertainty because of errors in observations, maintenance induced error, and other errors. In this investigation, we have considered these uncertainties as interval/fuzzy, and a method, namely double parametric form of fuzzy numbers are used to solve the uncertain fractional vibration model of order α(1<α≤2). The titled problem has been solved under various cases using the Residual power series method (RPSM). The performance of the present method is well in terms of computational efficiency. The consistency of the method is displayed by providing numerical solutions for various cases. Obtained results are depicted in terms of figures and are also compared with individual cases.

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Section: Introductionmentioning

confidence: 99%

Analysis of time‐fractional fuzzy vibration equation of large membranes using double parametric based Residual power series method

Jena

Sedighi

2020

Z Angew Math Mech

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Application of the Optimal Homotopy Asymptotic Approach for Solving Two-Point Fuzzy Ordinary Differential Equations of Fractional Order Arising in Physics

Jameel

Hashim²,

Anakira

et al. 2023

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This work focuses on solving and analyzing two-point fuzzy boundary value problems in the form of fractional ordinary differential equations (FFOBVPs) using a new version of the approximation analytical approach. FFOBVPs are useful in describing complex scientific phenomena that include heritable characteristics and uncertainty, and obtaining exact or close analytical solutions for these equations can be challenging, especially in the case of nonlinear problems. To address these difficulties, the optimal homotopy asymptotic method (OHAM) was studied and extended in a new form to solve FFOBVPs. The OHAM is known for its ability to solve both linear and nonlinear fractional models and provides a straightforward methodology that uses multiple convergence control parameters to optimally manage the convergence of approximate series solutions. The new form of the OHAM presented in this work incorporates the concepts of fuzzy sets theory and some fractional calculus principles to include fuzzy analysis in the method. The steps of fuzzification and defuzzification are used to transform the fuzzy problem into a crisp problem that can be solved using the OHAM. The method is demonstrated by solving and analyzing linear and nonlinear FFOBVPs at different values of fractional derivatives. The results obtained using the new form of the fuzzy OHAM are analyzed and compared to those found in the literature to demonstrate the method’s efficiency and high accuracy in the fuzzy domain. Overall, this work presents a feasible and efficient approach for solving FFOBVPs using a new form of the OHAM with fuzzy analysis.

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Solution Method for Systems of Nonlinear Fractional Differential Equations Using Third Kind Chebyshev Wavelets

Polat

Ocak

2023

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Chebyshev Wavelets of the third kind are proposed in this study to solve nonlinear systems of FDEs. The main goal of the method is to convert the nonlinear FDE into a nonlinear system of algebraic equations that can be easily solved using matrix methods. In order to achieve this, we first generate the operational matrices for the fractional integration using third kind Chebyshev Wavelets and block-pulse functions (BPF) for function approximation. Since the obtained operational matrices are sparse, the obtained numerical method is fast and computationally efficient. The original nonlinear FDE is transformed into a system of algebraic equations in a vector-matrix form using the obtained operational matrices. The collocation points are then used to solve the system of algebraic equations. Numerical results for various examples and comparisons are presented.

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New Implementation of Residual Power Series for Solving Fuzzy Fractional Riccati Equation

Cited by 3 publications

References 26 publications

Analysis of time‐fractional fuzzy vibration equation of large membranes using double parametric based Residual power series method

Analysis of time‐fractional fuzzy vibration equation of large membranes using double parametric based Residual power series method

Application of the Optimal Homotopy Asymptotic Approach for Solving Two-Point Fuzzy Ordinary Differential Equations of Fractional Order Arising in Physics

Solution Method for Systems of Nonlinear Fractional Differential Equations Using Third Kind Chebyshev Wavelets

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