Results 11 to 20 of about 621,794 (386)
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. Self-consistency involves proving generalizations of all fundamental theorems of vector calculus for generalized kernels of ...
Vasily E. Tarasov
doaj +5 more sources
Fractional calculus in mathematical oncology. [PDF]
Sci Rep, 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 ...
Alinei-Poiana T, Dulf EH, Kovacs L.
europepmc +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
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
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
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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
Generalized fractional calculus with applications to the calculus of variations
Computers & Mathematics with Applications, 2012 Submitted 22-Dec-2011; revised 26-Jan-2012; accepted 27-Jan-2012; for publication in Computers and Mathematics with ...
Odzijewicz, Tatiana +2 more
openaire +6 more sources
Calculus of Variations with Classical and Fractional Derivatives [PDF]
, 2012 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
Odzijewicz, Tatiana +1 more
core +4 more sources
Artificial neural networks: a practical review of applications involving fractional calculus. [PDF]
Eur Phys J Spec Top, 2022 In this work, a bibliographic analysis on artificial neural networks (ANNs) using fractional calculus (FC) theory has been developed to summarize the main features and applications of the ANNs. ANN is a mathematical modeling tool used in several sciences
Viera-Martin E +4 more
europepmc +2 more sources
Fractional Calculus and the Future of Science. [PDF]
Entropy (Basel), 2021 The invitation to contribute to this anthology of articles on the fractional calculus (FC) encouraged submissions in which the authors look behind the mathematics and examine what must be true about the phenomenon to justify the replacement of an integer-order derivative with a non-integer-order (fractional) derivative (FD) before discussing ways to ...
West BJ.
europepmc +5 more sources