Existence Results for a New Class of Nonlinear Langevin Equations of Fractional Orders

2019 ◽  
Vol 43 (5) ◽  
pp. 2335-2342
Author(s):  
Yasser Khalili ◽  
Milad Yadollahzadeh
Keyword(s):  
Existence Results ◽  
Langevin Equations ◽  
New Class ◽  
Fractional Orders ◽  
Nonlinear Langevin Equations

scholarly journals Measure of noncompactness for an infinite system of fractional Langevin equation in a sequence space

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed Salem ◽  
Hashim M. Alshehri ◽  
Lamya Almaghamsi
Keyword(s):  
Sequence Space ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Existence Results ◽  
Langevin Equations ◽  
Point Boundary ◽  
Hausdorff Measure Of Noncompactness ◽  
Generalized Derivative ◽  
Fractional Langevin Equation ◽  
Fractional Orders

AbstractA new sequence space related to the space $\ell _{p}$ ℓ p , $1\leq p<\infty $ 1 ≤ p < ∞ (the space of all absolutely p-summable sequences) is established in the present paper. It turns out that it is Banach and a BK space with Schauder basis. The Hausdorff measure of noncompactness of this space is presented and proven. This formula with the aid the Darbo’s fixed point theorem is used to investigate the existence results for an infinite system of Langevin equations involving generalized derivative of two distinct fractional orders with three-point boundary condition.

scholarly journals On D-KKM theorem and its applications

2003 ◽  
Vol 67 (1) ◽  
pp. 67-77 ◽  
Author(s):  
H. K. Pathak ◽  
M. S. Khan
Keyword(s):  
Variational Inequalities ◽  
Existence Results ◽  
Kkm Theorem ◽  
Maximal Elements ◽  
New Class ◽  
Kkm Mappings ◽  
Set Valued Mappings ◽  
Convex Setting

In this paper, we introduce a new class of set-valued mappings in a non-convex setting called D-KKM mappings and prove a general D-KKM theorem. This extends and improves the KKM theorem for several families of set-valued mappings, such as (X, Y), C(X, Y), C (X, Y), C (X, Y) and C (X, Y). In the sequel, we apply our theorem to get some existence results for maximal elements, generalised variational inequalities, and price equilibria.

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