scholarly journals Variable Order Mittag–Leffler Fractional Operators on Isolated Time Scales and Application to the Calculus of Variations

2019 ◽  
pp. 35-47
Author(s):  
Thabet Abdeljawad ◽  
Raziye Mert ◽  
Delfim F. M. Torres
Keyword(s):  
Calculus Of Variations ◽  
Time Scales ◽  
Variable Order ◽  
Fractional Operators

scholarly journals Applications of Distributed-Order Fractional Operators: A Review

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 110
Author(s):  
Wei Ding ◽  
Sansit Patnaik ◽  
Sai Sidhardh ◽  
Fabio Semperlotti
Keyword(s):  
Fractional Calculus ◽  
Real World ◽  
Transport Processes ◽  
Model Systems ◽  
Variable Order ◽  
Fractional Operators ◽  
Research Activity ◽  
Road Map ◽  
Real World Applications ◽  
Distributed Order

Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader area of fractional calculus that has important and far-reaching applications for the modeling of complex systems. DOFC generalizes the intrinsic multiscale nature of constant and variable-order fractional operators opening significant opportunities to model systems whose behavior stems from the complex interplay and superposition of nonlocal and memory effects occurring over a multitude of scales. In recent years, a significant amount of studies focusing on mathematical aspects and real-world applications of DOFC have been produced. However, a systematic review of the available literature and of the state-of-the-art of DOFC as it pertains, specifically, to real-world applications is still lacking. This review article is intended to provide the reader a road map to understand the early development of DOFC and the progressive evolution and application to the modeling of complex real-world problems. The review starts by offering a brief introduction to the mathematics of DOFC, including analytical and numerical methods, and it continues providing an extensive overview of the applications of DOFC to fields like viscoelasticity, transport processes, and control theory that have seen most of the research activity to date.

scholarly journals Higher-Order Calculus of Variations on Time Scales

2008 ◽  
pp. 149-159 ◽  
Author(s):  
Rui A. C. Ferreira ◽  
Delfim F. M. Torres
Keyword(s):  
Calculus Of Variations ◽  
Time Scales ◽  
Higher Order

scholarly journals Calculus of variations on time scales: applications to economic models

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Małgorzata Guzowska ◽  
Agnieszka B Malinowska ◽  
Moulay Rchid Sidi Ammi
Keyword(s):  
Calculus Of Variations ◽  
Time Scales ◽  
Economic Models

Synthesis of multifractional Gaussian noises based on variable-order fractional operators

2011 ◽  
Vol 91 (7) ◽  
pp. 1645-1650 ◽  
Author(s):  
Hu Sheng ◽  
Hongguang Sun ◽  
YangQuan Chen ◽  
TianShuang Qiu
Keyword(s):  
Variable Order ◽  
Fractional Operators

scholarly journals Calculus of variations on time scales with nabla derivatives

2009 ◽  
Vol 71 (12) ◽  
pp. e763-e773 ◽  
Author(s):  
Natália Martins ◽  
Delfim F.M. Torres
Keyword(s):  
Calculus Of Variations ◽  
Time Scales
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