Fibonacci Polynomial Approach for Solving a Class of Fractional Differential Equations with Proportional Caputo Derivative

In this paper, a numerical solution method to solve fractional differential equations with proportional Caputo derivative is introduced. Fibonacci collocation method is applied to a class of fractional differential equations. In order to show the efficiency of the proposed method, two illustrative examples are presented by tables and graphical forms. After observation the tables and graphics, it is concluded that Fibonacci collocation method gives very good and robust approximation results for the class of investigated fractional differential equations.

[1]  Amir Khan,et al.  Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function , 2021, Advances in difference equations.

[2]  D. Baleanu,et al.  Effects of hybrid nanofluid on novel fractional model of heat transfer flow between two parallel plates , 2021 .

[3]  Ali Akgül,et al.  New Illustrative Applications of Integral Transforms to Financial Models with Different Fractional Derivatives , 2021 .

[4]  Abdon Atangana,et al.  A novel Covid-19 model with fractional differential operators with singular and non-singular kernels: Analysis and numerical scheme based on Newton polynomial , 2021, Alexandria Engineering Journal.

[5]  D. Baleanu,et al.  A hybrid stochastic fractional order Coronavirus (2019-nCov) mathematical model , 2021, Chaos, Solitons & Fractals.

[6]  H. Dutta,et al.  Analysis of a fractional HIV model with Caputo and constant proportional Caputo operators , 2020 .

[7]  D. Baleanu,et al.  Laplace Transform Method for Economic Models with Constant Proportional Caputo Derivative , 2020, Fractal and Fractional.

[8]  Dumitru Baleanu,et al.  On a Fractional Operator Combining Proportional and Classical Differintegrals , 2020, Mathematics.

[9]  A. Atangana,et al.  Thermal stratification of rotational second-grade fluid through fractional differential operators , 2020, Journal of Thermal Analysis and Calorimetry.

[10]  Veysel Fuat Hatipoğlu,et al.  Cobweb model with conformable fractional derivatives , 2018 .

[11]  Veysel Fuat Hatipoğlu.  A numerical algorithm for the solution of nonlinear fractional differential equations via beta‐derivatives , 2018, Mathematical Methods in the Applied Sciences.

[12]  Veysel Fuat Hatipoğlu,et al.  An efficient scheme for solving a system of fractional differential equations with boundary conditions , 2017 .

[13]  Farshid Mirzaee,et al.  A new collocation approach for solving systems of high-order linear Volterra integro-differential equations with variable coefficients , 2017, Appl. Math. Comput..

[14]  Veysel Fuat Hatipoğlu,et al.  Approximate solutions of Volterra-Fredholm integro-differential equations of fractional order , 2017 .

[15]  Farshid Mirzaee,et al.  Solving systems of linear Fredholm integro-differential equations with Fibonacci polynomials , 2014 .

[16]  M. Sezer,et al.  FIBONACCI COLLOCATION METHOD FOR SOLVING LINEAR DIFFERENTIAL - DIFFERENCE EQUATIONS , 2013 .

[17]  Mehmet Sezer,et al.  Fibonacci Collocation Method for Solving High-Order Linear Fredholm Integro-Differential-Difference Equations , 2013, Int. J. Math. Math. Sci..

[18]  Ángel Plaza,et al.  On k-Fibonacci sequences and polynomials and their derivatives , 2009 .

[19]  Ángel Plaza,et al.  The k-Fibonacci sequence and the Pascal 2-triangle , 2007 .

[20]  Farshid Mirzaee,et al.  Solving singularly perturbed differential-difference equations arising in science and engineering with Fibonacci polynomials , 2013 .