Existence results for fractional semilinear differential inclusions in Banach spaces

Liu, Xiaoyou; Liu, Zhenhai

doi:10.1007/s12190-012-0634-0

Cited by 13 publications

(3 citation statements)

References 23 publications

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“…Fractional advectiondispersion equations are used to model many problems in physics, biology, and finance [3][4][5]. Fractional differential equations have attracted fantastic attention of many authors in recent years [6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions

Liu

Hou

2017

Advances in Mathematical Physics

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Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of ( ) and computational cost of ( log ). Traditionally, the Gaussian elimination method requires storage of ( 2 ) and computational cost of ( 3 ). Finally, the accuracy and efficiency of the method are checked with a numerical example.

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Section: Introductionmentioning

confidence: 99%

A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions

Liu

Hou

2017

Advances in Mathematical Physics

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“…of differential inclusions [5][6][7]29,30]. El-Sayed and Ibrahim [12] initiated the study of FDI and consequently various results have been developed, see [1,21,[37][38][39][40][41]. However, only very few works are available in the existing literature for dealing fractional differential inclusions.…”

Section: Introductionmentioning

confidence: 99%

Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi’s function

Balasubramaniam

Tamilalagan

2015

Applied Mathematics and Computation

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“…Moreover, physical systems can be represented more accurately through fractional derivative formulation. On the other hand, the fractional differential inclusions arise in the mathematical modeling of certain problems in economics, optimal controls, etc., so the problem of existence of solutions of fractional differential inclusions has been studied by several authors for different kind of problems (see [3][4][5]19] and the references therein). In particular, delay fractional differential inclusions arise in many physical and biological applications, but often demand the use of non-constant or state-dependent delays.…”

Section: Introductionmentioning

confidence: 99%

Existence of Solutions for Fractional Partial Neutral Stochastic Functional Integro-Differential Inclusions with State-Dependent Delay and Analytic Resolvent Operators

Guendouzi

Bousmaha

2015

Vietnam J. Math.

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We investigate the existence of mild solutions for a class of fractional partial neutral stochastic functional integro-differential inclusions with state-dependent delay and analytic α-resolvent operators in Hilbert spaces. Sufficient conditions for the existence are established by using the nonlinear alternative of Leray-Schauder type for multivalued maps due to O'Regan and the fractional power of operators. An example is provided to illustrate the obtained theory.Keywords Stochastic integro-differential inclusions · State-dependent delay · Multi-valued map · Fractional neutral integro-differential inclusions · α-resolvent operator Mathematics Subject Classification (2010) 34A37 · 60H10 · 34K50 · 34G25 · 26A33

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Existence results for fractional semilinear differential inclusions in Banach spaces

Cited by 13 publications

References 23 publications

A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions

A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions

Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi’s function

Existence of Solutions for Fractional Partial Neutral Stochastic Functional Integro-Differential Inclusions with State-Dependent Delay and Analytic Resolvent Operators

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