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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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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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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Delay-Dependent Stability Criterion of Caputo Fractional Neural Networks with Distributed Delay [PDF]
Discrete Dynamics in Nature and Society, 2014 This paper is concerned with the finite-time stability of Caputo fractional neural networks with distributed delay. The factors of such systems including Caputo’s fractional derivative and distributed delay are taken into account synchronously.
Abdulaziz Alofi +3 more
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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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A Note on Caputo’s Derivative Operator Interpretation in Economy
Journal of Applied Mathematics, 2018 We propound the economic idea in terms of fractional derivatives, which involves the modified Caputo’s fractional derivative operator. The suggested economic interpretation is based on a generalization of average count and marginal value of economic ...
Hameed Ur Rehman +2 more
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Multiplicity Result of Positive Solutions for Nonlinear Differential Equation of Fractional Order [PDF]
Abstract and Applied Analysis, 2012 We investigate the existence of multiple positive solutions for a class of boundary value problems of nonlinear differential equation with Caputo’s fractional order derivative. The existence results are obtained by means of the Avery-Peterson fixed point
Yang Liu, Zhang Weiguo
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An efficient fractional polynomial method for space fractional diffusion equations
Ain Shams Engineering Journal, 2018 In this paper, we develop a new approximation technique for solving space fractional diffusion equation. The method of solution is based on fractional order Legendre function with the concept of Caputo’s definition of fractional derivatives.
K. Krishnaveni +3 more
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Existence of positive solutions to a coupled system of fractional hybrid differential equations [PDF]
Matrix Science Mathematic, 2018 where Dα is the Caputo’s fractional derivative of order α ,1 0 and the functions f : j × R × R → R , f (0,0) = 0 and g : j × R× R → R satisfy certain conditions.
Ghulam Hussain +2 more
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Solvability of Some Fractional Boundary Value Problems with a Convection Term
Discrete Dynamics in Nature and Society, 2019 This paper is devoted to the research of some Caputo’s fractional derivative boundary value problems with a convection term. By the use of some fixed-point theorems and the properties of Green function, the existence results of at least one or triple ...
Yongfang Wei, Zhanbing Bai
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