scholarly journals Existence results for a multipoint boundary value problem of nonlinear sequential Hadamard fractional differential equations

Cubo (Temuco) ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 225-237
Author(s):  
Bashir Ahmad ◽  
Amjad F. Albideewi ◽  
Sotiris K. Ntouyas ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Existence Results ◽  
Multipoint Boundary ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential ◽  
Multipoint Boundary Value Problem

The method of upper and lower solutions for integral boundary value problem of semilinear fractional differential equations with non-instantaneous impulses

2020 ◽  
Vol 70 (3) ◽  
pp. 625-640 ◽  
Author(s):  
Mengrui Xu ◽  
Shurong Sun ◽  
Zhenlai Han
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Existence Results ◽  
Three Solutions ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Fractional Differential

AbstractIn this paper, we investigate a class of semilinear fractional differential equations with non-instantaneous impulses and integral boundary value conditions. By the method of upper and lower solutions combined with Amann three-solution theorem, existence results of at least three solutions are obtained.

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 Singular Positone and Semipositone Boundary Value Problems of Nonlinear Fractional Differential Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Chengjun Yuan ◽  
Daqing Jiang ◽  
Xiaojie Xu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Real Number ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

We present some new existence results for singular positone and semipositone nonlinear fractional boundary value problemD0+αu(t)=μa(t)f(t,u(t)), 0<t<1,u(0)=u(1)=u′(0)=u′(1)=0, whereμ>0,a,andfare continuous,α∈(3,4]is a real number, andD0+αis Riemann-Liouville fractional derivative. Throughout our nonlinearity may be singular in its dependent variable. Two examples are also given to illustrate the main 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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