scholarly journals Existence Results for a Coupled System of Nonlinear Fractional Differential Equation with Four-Point Boundary Conditions

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
M. Gaber ◽  
M. G. Brikaa
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Existence Result ◽  
Coupled System ◽  
Existence Results ◽  
Point Boundary ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential

This paper studies a coupled system of nonlinear fractional differential equation with four-point boundary conditions. Applying the Schauder fixed-point theorem, an existence result is proved for the following system: , , , , , , , , where satisfy certain conditions.

Lyapunov-type inequalities for nonlinear fractional differential equation with Hilfer fractional derivative under multi-point boundary conditions

2018 ◽  
Vol 21 (3) ◽  
pp. 833-843 ◽  
Author(s):  
Youyu Wang ◽  
Qichao Wang
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Point Boundary ◽  
Hilfer Fractional Derivative ◽  
Nonlinear Fractional Differential Equation ◽  
Early Results ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems

Abstract In this work, we establish Lyapunov-type inequalities for the fractional boundary value problems with Hilfer fractional derivative under multi-point boundary conditions, the results are new and generalize and improve some early results in the literature.

Existence result for nonlinear fractional differential equations with nonlocal fractional integro-differential boundary conditions in Banach spaces

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Djamila Seba ◽  
Hamza Rebai ◽  
Johnny Henderson
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Existence Result ◽  
Nonlinear Fractional Differential Equation ◽  
Measures Of Noncompactness ◽  
Fractional Differential

Abstract The nonlinear fractional differential equation with nonlocal fractional integro-differential boundary conditions in Banach spaces is studied, an existence result is obtained by using the method associated with the technique of measures of noncompactness and an appropriate fixed point theorem. An example is given to illustrate the theory.

scholarly journals On Antiperiodic Nonlocal Three-Point Boundary Value Problems for Nonlinear Fractional Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Bashir Ahmad ◽  
Jorge Losada ◽  
Juan J. Nieto
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Existence Results ◽  
Point Boundary ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential ◽  
The Given

We introduce boundary value conditions involving antiperiodic and nonlocal three-point boundary conditions. We solve a nonlinear fractional differential equation supplemented with those conditions. We obtain some existence results for the given problem by applying some standard tools of fixed point theory. These results are well illustrated with the aid of examples.

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