Application of a time-fractal fractional derivative with a power-law kernel to the Burke-Shaw system based on Newton's interpolation polynomials [PDF]
MethodsXThis paper proposes some updated and improved numerical schemes based on Newton's interpolation polynomial. A Burke-Shaw system of the time-fractal fractional derivative with a power-law kernel is presented as well as some illustrative examples. To solve
Najat Almutairi, Sayed Saber
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The General Solution of Singular Fractional-Order Linear Time-Invariant Continuous Systems with Regular Pencils [PDF]
Entropy, 2018 This paper introduces a general solution of singular fractional-order linear-time invariant (FoLTI) continuous systems using the Adomian Decomposition Method (ADM) based on the Caputo's definition of the fractional-order derivative.
Iqbal M. Batiha +3 more
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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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Fractional variational problems with the Riesz-Caputo derivative
Applied Mathematics Letters, 2012 In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the ...
Almeida, R. +2 more
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Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference [PDF]
Abstract and Applied Analysis, 2010 The qualitative behavior of a perturbed fractional-order differential equation with Caputo's derivative that differs in initial position and initial time with respect to the unperturbed fractional-order differential equation with Caputo's derivative has ...
Coşkun Yakar
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On the existence of mild solutions for nonconvex fractional semilinear differential inclusions [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2012 We establish some Filippov type existence theorems for solutions of fractional semilinear differential inclusions involving Caputo's fractional derivative in Banach spaces.
Aurelian Cernea
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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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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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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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Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay [PDF]
Abstract and Applied Analysis, 2010 Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and ...
S. J. Sadati +4 more
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