Theoretical and numerical analysis of monotonicity results for fractional difference operators

2021 ◽  
pp. 107104
Author(s):  
Rajendra Dahal ◽  
Christopher S. Goodrich
Keyword(s):  
Numerical Analysis ◽  
Difference Operators ◽  
Fractional Difference ◽  
Theoretical And Numerical Analysis ◽  
Monotonicity Results

scholarly journals Monotonicity results for delta and nabla caputo and Riemann fractional differences via dual identities

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3671-3683 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Bahaaeldin Abdalla
Keyword(s):  
Difference Operators ◽  
Fractional Difference ◽  
Monotonicity Properties ◽  
Delta Type ◽  
Dual Identities ◽  
The Right ◽  
Monotonicity Results

Recently, some authors have proved monotonicity results for delta and nabla fractional differences separately. In this article, we use dual identities relating delta and nabla fractional difference operators to prove shortly the monotonicity properties for the (left Riemann) nabla fractional differences using the corresponding delta type properties. Also, we proved some monotonicity properties for the Caputo fractional differences. Finally, we use the Q??operator dual identities to prove monotonicity results for the right fractional difference operators.

scholarly journals Theoretical and numerical analysis of the evaporation of mono- and multicomponent single fuel droplets

2021 ◽  
Vol 910 ◽  
Author(s):  
Alejandro Millán-Merino ◽  
Eduardo Fernández-Tarrazo ◽  
Mario Sánchez-Sanz
Keyword(s):  
Numerical Analysis ◽  
Fuel Droplets ◽  
Theoretical And Numerical Analysis

Abstract

scholarly journals Theoretical and numerical analysis of novel COVID-19 via fractional order mathematical model

2021 ◽  
Vol 20 ◽  
pp. 103676
Author(s):  
Amjad Ali ◽  
Muhammad Yasin Khan ◽  
Muhammad Sinan ◽  
F.M. Allehiany ◽  
Emad E. Mahmoud ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Numerical Analysis ◽  
Fractional Order ◽  
Theoretical And Numerical Analysis

scholarly journals Discrete fractional order two-point boundary value problem with some relevant physical applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
R. Dhineshbabu ◽  
S. Rashid ◽  
M. Rehman
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Difference Operators ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Fractional Difference ◽  
Rassias Stability

Abstract The results reported in this paper are concerned with the existence and uniqueness of solutions of discrete fractional order two-point boundary value problem. The results are developed by employing the properties of Caputo and Riemann–Liouville fractional difference operators, the contraction mapping principle and the Brouwer fixed point theorem. Furthermore, the conditions for Hyers–Ulam stability and Hyers–Ulam–Rassias stability of the proposed discrete fractional boundary value problem are established. The applicability of the theoretical findings has been demonstrated with relevant practical examples. The analysis of the considered mathematical models is illustrated by figures and presented in tabular forms. The results are compared and the occurrence of overlapping/non-overlapping has been discussed.

Orlicz lacunary sequence spaces of 𝑙-fractional difference operators

2020 ◽  
Vol 26 (2) ◽  
pp. 173-183
Author(s):  
Kuldip Raj ◽  
Kavita Saini ◽  
Anu Choudhary
Keyword(s):  
Difference Operator ◽  
Lacunary Sequence ◽  
Sequence Spaces ◽  
Difference Operators ◽  
Normed Spaces ◽  
Fractional Difference ◽  
New Approach ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
Bounded Sequences

AbstractRecently, S. K. Mahato and P. D. Srivastava [A class of sequence spaces defined by 𝑙-fractional difference operator, preprint 2018, http://arxiv.org/abs/1806.10383] studied 𝑙-fractional difference sequence spaces. In this article, we intend to make a new approach to introduce and study some lambda 𝑙-fractional convergent, lambda 𝑙-fractional null and lambda 𝑙-fractional bounded sequences over 𝑛-normed spaces. Various algebraic and topological properties of these newly formed sequence spaces have been explored, and some inclusion relations concerning these spaces are also established. Finally, some characterizations of the newly formed sequence spaces are given.

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