Results 31 to 40 of about 60,684 (330)
The Variable-Order Fractional Calculus of Variations
, 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
Almeida, Ricardo +2 more
core +1 more source
Partial Differential Equations in Applied MathematicsThe dynamics of viscous fluids may be elucidated via the Navier–Stokes equations, which create a fundamental relationship between the exertion of external forces upon fluid motion and the resultant fluid pressure.
P. Dunnimit +2 more
doaj +1 more source
N-FRACTIONAL CALCULUS OPERATOR METHOD TO THE EULER EQUATION
Проблемы анализа, 2018 We can obtain the explicit solutions of the Euler equation by using the fractional calculus methods. So, we apply the N operator method in the fractional calculus to solve this equation in this paper.
R. Yilmazer, O. Ozturk
doaj +1 more source
Partial Differential Equations in Applied MathematicsThe Navier–Stokes equations describe the behavior of viscous fluids and establish a fundamental connection between the application of external forces on fluid motion and the resulting pressure within the fluid. The objective of this study is to solve the
W. Sawangtong +3 more
doaj +1 more source
Weighted Fractional Calculus: A General Class of Operators
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 +1 more source
Fractional-calculus diffusion equation [PDF]
Nonlinear Biomedical Physics, 2010 Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems.The canonical quantization of a system represented classically by one-dimensional Fick's law, and the ...
Hussam Alrabaiah, Abdul-Wali Ajlouni
openaire +3 more sources
Joining Spacetimes on Fractal Hypersurfaces
, 2018 The theory of fractional calculus is attracting a lot of attention from mathematicians as well as physicists. The fractional generalisation of the well-known ordinary calculus is being used extensively in many fields, particularly in understanding ...
Anand, Ankit, Chatterjee, Ayan
core +1 more source
Coupled systems of fractional equations related to sound propagation: analysis and discussion [PDF]
, 2012 In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in the ...
Diethelm K. +6 more
core +1 more source
Concavity in fractional calculus
Filomat, 2018 We discuss a concavity like property for functions u satisfying D?0+u ? C[0, b] with u(0) = 0 and -D?0+u(t) ? 0 for all t ? [0,b]. We develop the property for ? ? (1,2], where D?0+ is the standard Riemann-Liouville fractional derivative. We observe the property is also valid in the case ? = 1. Finally, we show that under certain conditions,
Eloe, Paul W., Neugebauer, Jeffrey T.
openaire +2 more sources
Bielecki-Ulam stability of a hammerstein-type difference system
MethodsXIn this study, we investigate the Bielecki-Ulam (B-U) stabilities of two forms of Hammerstein-type difference systems (HT-DS). Specifically, we consider the systems:(0.1){xm+1−xm=M¯mxm+F¯(m,xm,xhm)[∑[j=0][m]G¯(m,j)H¯(j,xj,xhj)]x0=b0,and(0.2){xm+1−xm=M ...
Gul Rahmat +5 more
doaj +1 more source