scholarly journals Existence of mild solutions for fractional differential equations in separable Banach space

2015 ◽  
pp. 489-501
Author(s):  
Adel Jawahdou
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Separable Banach Space ◽  
Mild Solutions ◽  
Fractional Differential

ANTI-PERIODIC TYPE BOUNDARY VALUE PROBLEMS FOR SINGULAR MULTI-TERM FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS

2013 ◽  
Vol 24 (06) ◽  
pp. 1350047 ◽  
Author(s):  
YUJI LIU
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Continuous Operator ◽  
Weighted Banach Space ◽  
Fractional Differential ◽  
The Fixed Point Theorem ◽  
Type Boundary

Results on the existence of solutions of anti-periodic type boundary value problems for singular multi-term fractional differential equations with impulse effects are established. We first transform the problem into a hybrid system, then construct a weighted Banach space and a completely continuous operator, and finally, we use the fixed point theorem in the Banach space to prove the main results. An example is given to illustrate the efficiency of the main theorems.

scholarly journals Multiplicity Solutions of Fractional Impulsive p -Laplacian Systems: New Result

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Rafik Guefaifia ◽  
Mohamed Abdalla ◽  
Tahar Bouali ◽  
Fares Kamache ◽  
Bahri Belkacem Cherif ◽  
...  
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Weak Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Perturbed Systems ◽  
Fractional Differential

In this paper, the existence of multiplicity distinct weak solutions is proved for differentiable functionals for perturbed systems of impulsive nonlinear fractional differential equations. Further, examples are given to show the feasibility and efficacy of the key findings. This work is an extension of the previous works to Banach space.

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