scholarly journals Numerical solution for a class of nonlinear variable order fractional differential equations with Legendre wavelets

2015 ◽  
Vol 46 ◽  
pp. 83-88 ◽  
Author(s):  
Yi-Ming Chen ◽  
Yan-Qiao Wei ◽  
Da-Yan Liu ◽  
Hao Yu
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Fractional Differential Equations ◽  
Variable Order ◽  
Legendre Wavelets ◽  
Fractional Differential

Fourth kind Chebyshev Wavelet Method for the solution of multi-term variable order fractional differential equations

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Arzu Turan Dincel ◽  
Sadiye Nergis Tural Polat
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Fractional Differential Equations ◽  
Real Life ◽  
Operational Matrices ◽  
Variable Order ◽  
Content Type ◽  
Coefficient Vector ◽  
Fractional Differential ◽  
Fourth Kind

PurposeMulti-term variable-order fractional differential equations (VO-FDEs) are powerful tools in accurate modeling of transient-regime real-life problems such as diffusion phenomena and nonlinear viscoelasticity. In this paper the Chebyshev polynomials of the fourth kind is employed to obtain a numerical solution for those multi-term VO-FDEs.Design/methodology/approachTo this end, operational matrices for the approximation of the VO-FDEs are obtained using the Fourth kind Chebyshev Wavelets (FKCW). Thus, the VO-FDE is condensed into an algebraic equation system. The solution of the system of those equations yields a coefficient vector, the coefficient vector in turn yields the approximate solution.FindingsSeveral examples that we present at the end of the paper emphasize the efficacy and preciseness of the proposed method.Originality/valueThe value of the paper stems from the exploitation of FKCWs for the numerical solution of multi-term VO-FDEs. The method produces accurate results even for relatively small collocation points. What is more, FKCW method provides a compact mapping between multi-term VO-FDEs and a system of algebraic equations given in vector-matrix form.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

Analytic approximate solutions for a class of variable order fractional differential equations using the polynomial least squares method

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Constantin Bota ◽  
Bogdan Căruntu
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Fractional Differential Equations ◽  
Least Squares Method ◽  
Approximate Solutions ◽  
Variable Order ◽  
Polynomial Solutions ◽  
Fractional Differential ◽  
Approximate Polynomial

AbstractIn this paper a new way to compute analytic approximate polynomial solutions for a class of nonlinear variable order fractional differential equations is proposed, based on the Polynomial Least Squares Method (PLSM). In order to emphasize the accuracy and the efficiency of the method several examples are included.

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