Results 21 to 30 of about 40,961 (259)
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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Fractional Divided Differences and the Solution of Differential Equations of Fractional Order
Advances in Applied Mathematics, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
David Elizarraraz, Luis Verde-Star
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Controlling fractional difference equations using feedback
Chaos, Solitons & Fractals, 2023 One of the most popular methods of controlling dynamical systems is feedback. It can be used without acquiring detailed knowledge of the underlying system. In this work, we study the stability of fractional-order linear difference equations under feedback. The stability results are derived for an arbitrary feedback time $τ$. We study the cases of $τ=1$
Divya D. Joshi +2 more
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Advances in Difference Equations, 2017 In this paper, we solve two-dimensional modified anomalous fractional sub-diffusion equation using modified implicit finite difference approximation. The stability and convergence of the proposed scheme are analyzed by the Fourier series method.
Umair Ali +2 more
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Entropy, 2020 This paper presents integer and linear time-invariant fractional order (FO) models of a closed-loop electric individual-wheel drive implemented on an autonomous platform. Two discrete-time FO models are tested: non-commensurate and commensurate.
Marcin Bąkała +4 more
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Advances in Difference Equations, 2021 By means of ς fractional sum operator, certain discrete fractional nonlinear inequalities are replicated in this text. Considering the methodology of discrete fractional calculus, we establish estimations of Gronwall type inequalities for unknown ...
Zareen A. Khan +3 more
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A Hilbert Space Approach to Fractional Difference Equations [PDF]
, 2020 We formulate fractional difference equations of Riemann-Liouville and Caputo type in a functional analytical framework. Main results are existence of solutions on Hilbert space-valued weighted sequence spaces and a condition for stability of linear fractional difference equations.
Anh, Pham The +7 more
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Numerical solution for space and time fractional order Burger type equation
Alexandria Engineering Journal, 2018 In this paper, we study the fractional differential operators thereby considering the space and time order Burger type equation with initial condition. The extended finite difference method which is based on shifted Grünwald, Caputo and Riemann formulas ...
Asıf Yokus
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Modeling with fractional difference equations
Journal of Mathematical Analysis and Applications, 2010 A fractional sum of a function \(f\) is introduced as \[ \Delta _{a}^{-\alpha}f(t)=\frac{1}{\Gamma (\alpha )}\sum_{s=a}^{t-\alpha }(t-s-1)^{(\alpha -1)}f(s), \] where \(a\in R,\) \(\alpha >0\), \(x^{(\alpha )}=\Gamma (x+1)/\Gamma (x-\alpha +1),\) \(f\) is defined for \(s=a\;(\text{mod }1),\) and \(\Delta _{a}^{-\alpha }f\) is defined for \(t=a+\alpha \;
Atıcı, Ferhan M., Şengül, Sevgi
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Nonlinear Analysis, 2023 A new fractional difference with an exponential kernel function is proposed in this study. First, a difference operator is defined by the exponential function.
Guang Yang, Guo-Cheng Wu, Hui Fu
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