scholarly journals Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1905
Author(s):  
Athasit Wongcharoen ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Nonlocal Integral Boundary Conditions

In this paper, we study boundary value problems for differential inclusions, involving Hilfer fractional derivatives and nonlocal integral boundary conditions. New existence results are obtained by using standard fixed point theorems for multivalued analysis. Examples illustrating our results are also presented.

scholarly journals Existence Results for Langevin Fractional Differential Inclusions Involving Two Fractional Orders with Four-Point Multiterm Fractional Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusions ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Fractional Differential Inclusions ◽  
Integral Boundary ◽  
Fractional Differential ◽  
The Right ◽  
Fractional Orders

We discuss the existence of solutions for Langevin fractional differential inclusions involving two fractional orders with four-point multiterm fractional integral boundary conditions. Our study relies on standard fixed point theorems for multivalued maps and covers the cases when the right-hand side of the inclusion has convex as well as nonconvex values. Illustrative examples are also presented.

scholarly journals The positive solutions of fractional differential equation with Riemann-Stieltjes integral boundary conditions

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2383-2394
Author(s):  
Xiaohan Zhang ◽  
Xiping Liu ◽  
Mei Jia ◽  
Haoliang Chen
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Stieltjes Integral ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Integral Boundary Value Problems ◽  
Ordered Banach Spaces

In this paper, we study a class of fractional differential equations with Riemann-Stieltjes integral boundary conditions. The existence and uniqueness of positive solutions for the boundary value problem are obtained via the use of fixed point theorems on cones in partially ordered Banach spaces. Many of the multi-point and integral boundary value problems studied previously studied are also included in our results.

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