Smoothing transformation and spline collocation for linear fractional boundary value problems

2016 ◽  
Vol 283 ◽  
pp. 234-250 ◽  
Author(s):  
Marek Kolk ◽  
Arvet Pedas ◽  
Enn Tamme
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Spline Collocation ◽  
Fractional Boundary Value Problems ◽  
Smoothing Transformation

SOLVING TWO-POINT BOUNDARY VALUE PROBLEMS OF FRACTIONAL DIFFERENTIAL EQUATIONS VIA SPLINE COLLOCATION METHODS

2010 ◽  
Vol 01 (01) ◽  
pp. 117-132 ◽  
Author(s):  
NINGMING NIE ◽  
YANMIN ZHAO ◽  
MIN LI ◽  
XIANGTAO LIU ◽  
SALVADOR JIMÉNEZ ◽  
...  
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Numerical Experiments ◽  
Boundary Value ◽  
Collocation Methods ◽  
Existence And Uniqueness Theorem ◽  
Spline Collocation ◽  
Fractional Differential ◽  
Theoretical Results ◽  
Fractional Boundary Value Problems

In this article, we introduce spline collocation methods to solve fractional boundary value problems (BVPs). The existence and uniqueness theorem of collocation solutions is studied, and the error estimate of collocation solutions is discussed. Numerical experiments are presented to demonstrate the theoretical results.

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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