scholarly journals Existence and Hyers-Ulam type stability results for nonlinear coupled system of Caputo-Hadamard type fractional differential equations

2021 ◽  
Vol 6 (1) ◽  
pp. 168-194
Author(s):  
Subramanian Muthaiah ◽  
◽  
Dumitru Baleanu ◽  
Nandha Gopal Thangaraj ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Coupled System ◽  
Nonlinear Coupled System ◽  
Fractional Differential ◽  
Ulam Type Stability ◽  
Stability Results

scholarly journals A study of a nonlinear coupled system of three fractional differential equations with nonlocal coupled boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bashir Ahmad ◽  
Soha Hamdan ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Coupled System ◽  
Contraction Mapping Principle ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Nonlinear Coupled System ◽  
Coupled Boundary Conditions ◽  
Fractional Differential

AbstractIn this research we introduce and study a new coupled system of three fractional differential equations supplemented with nonlocal multi-point coupled boundary conditions. Existence and uniqueness results are established by using the Leray–Schauder alternative and Banach’s contraction mapping principle. Illustrative examples are also presented.

scholarly journals Impulsive Coupled System of Fractional Differential Equations with Caputo–Katugampola Fuzzy Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Leila Sajedi ◽  
Nasrin Eghbali ◽  
Hassen Aydi
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Stability Of Solutions ◽  
Fractional Differential ◽  
The Given ◽  
Stability Results ◽  
Rassias Stability

In this article, we investigate the existence, uniqueness, and different kinds of Ulam–Hyers stability of solutions of an impulsive coupled system of fractional differential equations by using the Caputo–Katugampola fuzzy fractional derivative. We applied the Perov-type fixed point theorem to prove the existence and uniqueness of the proposed system. Furthermore, the Ulam–Hyers–Rassias stability and Ulam–Hyers–Rassias–Mittag-Leffler’s stability results for the given system are discussed.

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.

scholarly journals EXISTENCE AND STABILITY RESULTS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH TWO CAPUTO FRACTIONAL DERIVATIVES

2019 ◽  
pp. 341
Author(s):  
Mohamed Houas ◽  
Mohamed Bezziou
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Contraction Mapping ◽  
Nonlocal Boundary ◽  
Stability Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Existence And Stability ◽  
Fractional Differential ◽  
Stability Results

In this paper, we discuss the existence, uniqueness and stability of solutions for a nonlocal boundary value problem of nonlinear fractional differential equations with two Caputo fractional derivatives. By applying the contraction mapping and O’Regan fixed point theorem, the existence results are obtained. We also derive the Ulam-Hyers stability of solutions. Finally, some examples are given to illustrate our results.

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