scholarly journals A Survey on Existence Results for Boundary Value Problems of Hilfer Fractional Differential Equations and Inclusions

Foundations ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 63-98 ◽  
Author(s):  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence Results ◽  
Fractional Differential ◽  
Differential Equations And Inclusions

This paper is a survey of the recent results of the author for various classes of boundary value problems for Hilfer fractional differential equations and inclusions of fractional order in (1,2] supplemented with different kinds of nonlocal boundary conditions.

scholarly journals On multi-term proportional fractional differential equations and inclusions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Wafa Shammakh ◽  
Hadeel Z. Alzumi ◽  
Zahra Albarqi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Differential Equations And Inclusions

AbstractThe aim of this paper is to study new nonlocal boundary value problems of fractional differential equations and inclusions supplemented with slit-strips integral boundary conditions. Based on the functional analysis tools, the existence results for a nonlinear boundary value problem involving a proportional fractional derivative are presented. In addition to that, the extension of the problem at hand to its inclusion case is discussed. The obtained results are very interesting and are well illustrated with examples.

On nonlinear neutral Liouville–Caputo-type fractional differential equations with Riemann–Liouville integral boundary conditions

2019 ◽  
Vol 25 (2) ◽  
pp. 119-130 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Nonlocal Boundary Conditions ◽  
Integral Boundary ◽  
Nonlinear Alternative ◽  
Fractional Differential ◽  
Differential Equations And Inclusions

Abstract This paper studies neutral Liouville–Caputo-type fractional differential equations and inclusions supplemented with nonlocal Riemann–Liouville-type integral boundary conditions. Sadovskii’s fixed point theorem is applied to establish the existence result for the single-valued case, while the multivalued case is investigated by using nonlinear alternative for contractive maps. Examples are constructed to illustrate the main results. The case of nonlinear nonlocal boundary conditions is also discussed.

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