Fractal Derivatives, Fractional Derivatives and q-Deformed Calculus [PDF]
Entropy, 2023 This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff’s concepts of fractional dimension geometry.
Airton Deppman +2 more
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Positive solutions of two-point boundary value problems of nonlinear fractional differential equation at resonance [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2011 This paper is concerned with a kind of nonlinear fractional differential boundary value problem at resonance with Caputo's fractional derivative. Our main approach is the recent Leggett-Williams norm-type theorem for coincidences due to O'Regan and Zima.
Aijun Yang, Helin Wang
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Positive solutions for higher-order nonlinear fractional differential equation with integral boundary condition [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2011 In this paper, we study a kind of higher-order nonlinear fractional differential equation with integral boundary condition. The fractional differential operator here is the Caputo's fractional derivative.
Aijun Yang, Helin Wang
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Nonlinear Engineering, 2023 A nonlinear Boussinesq equation under fractal fractional Caputo’s derivative is studied. The general series solution is calculated using the double Laplace transform with decomposition. The convergence and stability analyses of the model are investigated
Algahtani Obaid J.
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An efficient numerical technique for solving time fractional Burgers equation
Alexandria Engineering Journal, 2020 A finite difference scheme which depends on a new approximation based on an extended cubic B-spline for the second order derivative is used to calculate the numerical outcomes of time fractional Burgers equation.
Tayyaba Akram +4 more
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Results in Physics, 2021 The generalized ZK-Burgers equation has nonlinear characteristics of the governing equation and helps to understand nonlinear waves in many fluid problems of plasma mediums.
Naeem Faraz +4 more
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Series solution to fractional contact problem using Caputo’s derivative
Open Physics, 2021 In this article, contact problem with fractional derivatives is studied. We use fractional derivative in the sense of Caputo. We deploy penalty function method to degenerate the obstacle problem into a system of fractional boundary value problems (FBVPs).
Rafiq Muhammad +7 more
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Results on the controllability of Caputo’s fractional descriptor systems with constant delays [PDF]
Bulletin of the Polish Academy of Sciences: Technical Sciences, 2023 The paper investigates the controllability of fractional descriptor linear systems with constant delays in control. The Caputo fractional derivative is considered.
Beata Sikora
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Numerical solution of fredholm fractional integro-differential equation with right-sided caputo’s derivative using bernoulli polynomials operational matrix of fractional derivative [PDF]
, 2019 In this article, fractional integro-differential equation (FIDE) of Fredholm type involving right-sided Caputo’s fractional derivative with multi-fractional orders is considered.
Alexander, C. H. C. +4 more
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Analytical Solution for the Fractional Partial Differential Equations by Adomian Decomposition and Modified Decomposition Method [PDF]
Engineering and Technology Journal, 2013 In this paper, analytical solution of the fractional partial differential equation has been presented. The algorithm for the analytical solution for this equation is based on Adomian's decomposition and modified decomposition method.
Iman Isho Gorial
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