Stability analysis of multi-term fractional-differential equations with three fractional derivatives [PDF]
, 2020 Necessary and sufficient stability and instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives and constant coefficients. In both cases, fractional-order-dependent as well as fractional-order-independent characterisations of stability and instability properties are obtained ...
arxiv +1 more source
Wavelets operational methods for fractional differential equations and systems of fractional differential equations [PDF]
, 2017 In this thesis, new and effective operational methods based on polynomials and wavelets for the solutions of FDEs and systems of FDEs are developed.
A. H. Al-Bagawi, A. H. Al-Bagawi +8 more
core +2 more sources
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
Nonlocal Fractional Differential Equations and Applications [PDF]
Complex Analysis and Operator Theory, 2020 Boundary value problems for nonlocal fractional elliptic equations with parameter in Banach spaces are studied. Uniform $L_p$-separability properties and sharp resolvent estimates are obtained for elliptic equations in terms of fractional derivatives.
openaire +3 more sources
Existence of fractional differential equations
Journal of Mathematical Analysis and Applications, 2005 AbstractConsider the fractional differential equation Dαx=f(t,x), where α∈(0,1) and f(t,x) is a given function. We obtained a sufficient condition for the existence for the solutions of this equation, improving previously known results.
Cheng Yu, Guozhu Gao
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Fractional calculus and time-fractional differential equations: revisit and construction of a theory [PDF]
arXiv, 2022 For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of the operator theory in fractional Sobolev spaces. Our framework provides a feasible extension of the classical Caputo and the Riemann-Liouville derivatives within Sobolev spaces of fractional orders including negative ones.
arxiv
Solution of System of Linear Fractional Differential Equations with Modified derivative of Jumarie Type [PDF]
American Journal of Mathematical Analysis, 2015, 2015 Solution of fractional differential equations is an emerging area of present day research because such equations arise in various applied fields. In this paper we have developed analytical method to solve the system of fractional differential equations in-terms of Mittag-Leffler function and generalized Sine and Cosine functions, where the fractional ...
arxiv +1 more source
On the oscillation of fractional differential equations
Fractional Calculus and Applied Analysis, 2012 In this paper we initiate the oscillation theory for fractional differential equations. Oscillation criteria are obtained for a class of nonlinear fractional differential equations of the form $$D_a^q x + f_1 (t,x) = v(t) + f_2 (t,x),\mathop {\lim }\limits_{t \to a} J_a^{1 - q} x(t) = b_1 $$ , where Daq denotes the Riemann-Liouville differential
Grace, Said R. +3 more
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Fractional Complex Transform for Fractional Differential Equations [PDF]
Mathematical and Computational Applications, 2010 Fractional complex transform is proposed to convert fractional differential equations into ordinary differential equations, so that all analytical methods devoted to advanced calculus can be easily applied to fractional calculus. Two examples are given.
Zheng-Biao Li, Ji-Huan He
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Linear fractional differential equations and eigenfunctions of fractional differential operators [PDF]
Computational and Applied Mathematics, 2016 Eigenfunctions associated with Riemann–Liouville and Caputo fractional differential operators are obtained by imposing a restriction on the fractional derivative parameter. Those eigenfunctions can be used to express the analytical solution of some linear sequential fractional differential equations.
Eliana Contharteze Grigoletto +2 more
openaire +4 more sources