Results 1 to 10 of about 611,053 (243)
Calculus of variations with fractional derivatives and fractional integrals [PDF]
Applied Mathematics Letters 22 (2009) 1816--1820, 2009 We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.
Ricardo Almeida, Delfim F. M. Torres
arxiv +8 more sources
General Fractional Vector Calculus [PDF]
Mathematics, 2021 A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators.
Vasily E. Tarasov
doaj +5 more sources
General Fractional Calculus in Multi-Dimensional Space: Riesz Form
Mathematics, 2023 An extension of the general fractional calculus (GFC) is proposed as a generalization of the Riesz fractional calculus, which was suggested by Marsel Riesz in 1949.
Vasily E. Tarasov
doaj +2 more sources
Fractional calculus in mathematical oncology
Scientific Reports, 2023 AbstractEven though, nowadays, cancer is one of the leading causes of death, too little is known about the behavior of this disease due to its unpredictability from one patient to another. Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage ...
Tudor Alinei-Poiana +2 more
openaire +4 more sources
Weighted Fractional Calculus: A General Class of Operators [PDF]
Fractal and Fractional, 2022 We conduct a formal study of a particular class of fractional operators, namely weighted fractional calculus, and its extension to the more general class known as weighted fractional calculus with respect to functions.
Arran Fernandez, Hafiz Muhammad Fahad
doaj +2 more sources
The Variable-Order Fractional Calculus of Variations [PDF]
, 2018 This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter 1) and of the fractional calculus of variations (Chapter 2).
Almeida, Ricardo +2 more
arxiv +3 more sources
Research on Application of Fractional Calculus Operator in Image Underlying Processing
Fractal and FractionalFractional calculus extends traditional, integer-based calculus to include non-integer orders, offering a powerful tool for a range of engineering applications, including image processing.
Guo Huang +5 more
doaj +2 more sources
Series expansion in fractional calculus and fractional differential equations [PDF]
arXiv, 2009 Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this theorem, in this paper we introduce fractional series expansion method to fractional calculus.
Ming-Fan Li, Ji-Rong Ren, Tao Zhu
arxiv +3 more sources
Sets of Fractional Operators and Numerical Estimation of the Order of Convergence of a Family of Fractional Fixed-Point Methods [PDF]
Fractal and Fractional, 2021 Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a simple and ...
A. Torres-Hernandez, F. Brambila-Paz
doaj +2 more sources
Calculus of Variations with Classical and Fractional Derivatives [PDF]
, 2010 We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental problem of the
Tatiana Odzijewicz, Delfim F. M. Torres
openalex +5 more sources