scholarly journals Existence and uniqueness of positive solution to singular fractional differential equations

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Yongqing Wang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Differential Equations ◽  
Positive Solution ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential

scholarly journals Positive Solution to Nonzero Boundary Values Problem for a Coupled System of Nonlinear Fractional Differential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Jinhua Wang ◽  
Hongjun Xiang ◽  
Zhigang Liu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solution ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Banach Fixed Point Theorem ◽  
Boundary Values ◽  
Nonzero Boundary ◽  
Fractional Differential

We consider the existence and uniqueness of positive solution to nonzero boundary values problem for a coupled system of fractional differential equations. The differential operator is taken in the standard Riemann-Liouville sense. By using Banach fixed point theorem and nonlinear differentiation of Leray-Schauder type, the existence and uniqueness of positive solution are obtained. Two examples are given to demonstrate the feasibility of the obtained results.

scholarly journals Existence and uniqueness of positive solutions for nonlinear Caputo-Hadamard fractional differential equations

2021 ◽  
Vol 40 (1) ◽  
pp. 139-152
Author(s):  
Abdelouaheb Ardjouni
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solution ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Upper And Lower Solutions ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

We prove the existence and uniqueness of a positive solution of nonlinear Caputo-Hadamard fractional differential equations. In the process we employ the Schauder and Banach fixed point theorems and the method of upper and lower solutions to show the existence and uniqueness of a positive solution. Finally, an example is given to illustrate our results.

scholarly journals Fractional Singular Differential Systems of Lane–Emden Type: Existence and Uniqueness of Solutions

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 95
Author(s):  
Yazid Gouari ◽  
Zoubir Dahmani ◽  
Shan E. Farooq ◽  
Farooq Ahmad
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Caputo Derivative ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Differential Systems ◽  
Banach Contraction ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential

A coupled system of singular fractional differential equations involving Riemann–Liouville integral and Caputo derivative is considered in this paper. The question of existence and uniqueness of solutions is studied using Banach contraction principle. Furthermore, the question of existence of at least one solution is discussed. At the end, an illustrative example is given in details.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

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