Corrigendum to "To study blowing-up solutions of a nonlinear system of fractional differential equations"

2013 ◽  
Vol 43 (1) ◽  
pp. 104
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Blowing Up ◽  
Fractional Differential ◽  
Blowing Up Solutions

Blowing-up solutions to two-times fractional differential equations

2013 ◽  
Vol 286 (17-18) ◽  
pp. 1797-1804 ◽  
Author(s):  
Mokhtar Kirane ◽  
Abdelouhab Kadem ◽  
Amar Debbouche
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Blowing Up ◽  
Fractional Differential ◽  
Blowing Up Solutions

scholarly journals On a nonlinear system of Riemann-Liouville fractional differential equations with semi-coupled integro-multipoint boundary conditions

2021 ◽  
Vol 19 (1) ◽  
pp. 760-772
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Badrah Alghamdi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Numerical Examples ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

Abstract We study a nonlinear system of Riemann-Liouville fractional differential equations equipped with nonseparated semi-coupled integro-multipoint boundary conditions. We make use of the tools of the fixed-point theory to obtain the desired results, which are well-supported with numerical examples.

scholarly journals Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Fractional Integral ◽  
Operational Matrix ◽  
Classical Solutions ◽  
Operational Matrices ◽  
Fractional Differential

We present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the Bernstein polynomials (BPs). In the first method, we use the operational matrix of Caputo fractional derivative (OMCFD), and in the second one, we apply the operational matrix of Riemann-Liouville fractional integral (OMRLFI). The obtained results are in good agreement with each other as well as with the analytical solutions. We show that the solutions approach to classical solutions as the order of the fractional derivatives approaches 1.

scholarly journals Extension of Operational Matrix Technique for the Solution of Nonlinear System of Caputo Fractional Differential Equations Subjected to Integral Type Boundary Constrains

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1154
Author(s):  
Hammad Khalil ◽  
Murad Khalil ◽  
Ishak Hashim ◽  
Praveen Agarwal
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Algebraic Structure ◽  
Operational Matrix ◽  
Coupled System ◽  
Operational Matrices ◽  
Integral Type ◽  
Nonlinear Coupled System ◽  
Fractional Differential

We extend the operational matrices technique to design a spectral solution of nonlinear fractional differential equations (FDEs). The derivative is considered in the Caputo sense. The coupled system of two FDEs is considered, subjected to more generalized integral type conditions. The basis of our approach is the most simple orthogonal polynomials. Several new matrices are derived that have strong applications in the development of computational scheme. The scheme presented in this article is able to convert nonlinear coupled system of FDEs to an equivalent S-lvester type algebraic equation. The solution of the algebraic structure is constructed by converting the system into a complex Schur form. After conversion, the solution of the resultant triangular system is obtained and transformed back to construct the solution of algebraic structure. The solution of the matrix equation is used to construct the solution of the related nonlinear system of FDEs. The convergence of the proposed method is investigated analytically and verified experimentally through a wide variety of test problems.

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