Numerical solution of a fractional differential equation arising in optics

Optik ◽  
2020 ◽  
Vol 208 ◽  
pp. 163911
Author(s):  
R. Alchikh ◽  
S.A. Khuri
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Fractional Differential Equation ◽  
Fractional Differential

NUMERICAL SOLUTION FOR THE FRACTIONAL REPLICATOR EQUATION

2005 ◽  
Vol 16 (07) ◽  
pp. 1017-1025 ◽  
Author(s):  
E. AHMED ◽  
A. M. A. EL-SAYED ◽  
A. E. M. EL-MESIRY ◽  
H. A. A. EL-SAKA
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Fractional Differential Equation ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Replicator Equation ◽  
Fractional Differential

In this paper, we study the replicator equation for the hawk–dove (HD) and Prisoner's Dilemma (PD) games and generalized it to the fractional differential equation.

scholarly journals Numerical Solution of Fractional Volterra-Fredholm Integro-Differential Equation Using Lagrange Polynomials

2020 ◽  
Vol 17 (4) ◽  
pp. 1234
Author(s):  
Nour Salman ◽  
Muna Mansour Mustfaf
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Numerical Solution ◽  
Fractional Differential Equation ◽  
Lagrange Polynomial ◽  
Lagrange Polynomials ◽  
Fractional Differential ◽  
A New Technique ◽  
Special Case

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal method in solving these problems.

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