scholarly journals Nonlinear boundary value problems for fractional differential inclusions with Caputo-Hadamard derivatives on the half line

2021 ◽  
Vol 6 (6) ◽  
pp. 6278-6292
Author(s):  
Mouffak Benchohra ◽  
◽  
John R. Graef ◽  
Nassim Guerraiche ◽  
Samira Hamani ◽  
...  
Keyword(s):  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Half Line ◽  
Fractional Differential Inclusions ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
Fractional Differential

scholarly journals Nonlinear boundary value problems for mixed-type fractional equations and Ulam-Hyers stability

2020 ◽  
Vol 18 (1) ◽  
pp. 916-929
Author(s):  
Huiwen Wang ◽  
Fang Li
Keyword(s):  
Boundary Value Problems ◽  
Mixed Type ◽  
Fractional Derivatives ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
New Techniques ◽  
Fractional Equations ◽  
Nonlinear Boundary Value ◽  
Fractional Differential

Abstract In this article, we discuss the nonlinear boundary value problems involving both left Riemann-Liouville and right Caputo-type fractional derivatives. By using some new techniques and properties of the Mittag-Leffler functions, we introduce a formula of the solutions for the aforementioned problems, which can be regarded as a novelty item. Moreover, we obtain the existence result of solutions for the aforementioned problems and present the Ulam-Hyers stability of the fractional differential equation involving two different fractional derivatives. An example is given to illustrate our theoretical result.

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