Numerical Methods for Multi-term Fractional Boundary Value Problems

2013 ◽  
pp. 535-542
Author(s):  
N. J. Ford ◽  
M. L. Morgado
Keyword(s):  
Numerical Methods ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Fractional Boundary Value Problems

scholarly journals Fractional boundary value problems: Analysis and numerical methods

2011 ◽  
Vol 14 (4) ◽  
Author(s):  
Neville Ford ◽  
M. Morgado
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Uniqueness Of The Solution ◽  
Fractional Boundary Value Problems

AbstractIn this paper we consider nonlinear boundary value problems for differential equations of fractional order α, 0 < α < 1. We study the existence and uniqueness of the solution and extend existing published results. In the last part of the paper we study a class of prototype methods to determine their numerical solution.

scholarly journals Existence and uniqueness criteria for the higher-order Hilfer fractional boundary value problems at resonance

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yousef Gholami
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Higher Order ◽  
Coupled Systems ◽  
At Resonance ◽  
Uniqueness Criteria ◽  
Fractional Boundary Value Problems

Abstract This investigation is devoted to the study of a certain class of coupled systems of higher-order Hilfer fractional boundary value problems at resonance. Combining the coincidence degree theory with the Lipschitz-type continuity conditions on nonlinearities, we present some existence and uniqueness criteria. Finally, to practically implement the obtained theoretical criteria, we give an illustrative application.

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