Boundary value problem defined by system of generalized Sturm–Liouville and Langevin Hadamard fractional differential equations

2020 ◽  
Author(s):  
Amel Berhail ◽  
Nora Tabouche ◽  
Mohammed M. Matar ◽  
Jehad Alzabut
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Hadamard Fractional Differential Equations ◽  
Sturm Liouville ◽  
Fractional Differential

scholarly journals Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 896
Author(s):  
Snezhana Hristova ◽  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Kuratowski Measure Of Noncompactness ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability ◽  
Existence Criteria

A boundary value problem for Hadamard fractional differential equations of variable order is studied. Note the symmetry of a transformation of a system of differential equations is connected with the locally solvability which is the same as the existence of solutions. It leads to the necessity of obtaining existence criteria for a boundary value problem for Hadamard fractional differential equations of variable order. Also, the stability in the sense of Ulam–Hyers–Rassias is investigated. The results are obtained based on the Kuratowski measure of noncompactness. An example illustrates the validity of the observed results.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

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