Weighted pseudo almost automorphic mild solutions to semilinear fractional differential equations

Mophou, Gisèle

doi:10.1016/j.amc.2011.02.048

Cited by 33 publications

(19 citation statements)

References 31 publications

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“…The fractional derivative is understood in the RiemannLiouville sense. Mophou [63] investigated the existence and uniqueness of weighted pseudo almost automorphic mild solution to the fractional differential equation:…”

Section: International Journal Of Differential Equationsmentioning

confidence: 99%

“…However, in many papers (for instance, [11,[51][52][53][54][55][56][57][58][59][60][61][62][63][64]) on almost periodic type and almost automorphic type solutions to fractional differential equations, to be able to apply the well-known Banach contraction principle, a (locally) Lipschitz condition for the nonlinearity of corresponding fractional differential equations is needed. As can be seen, our results generalize those as well as related research and have more broad applications.…”

Section: International Journal Of Differential Equationsmentioning

confidence: 99%

“…For this reason, (6) has gotten a considerable attention in recent years (cf. [51][52][53][54][55][56][57][58][59][60][61][62][63][64][68][69][70][71] and the references therein).…”

Section: International Journal Of Differential Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Existence of Asymptotically Almost Automorphic Mild Solutions of Semilinear Fractional Differential Equations

Cao

Huang²,

N’Guérékata

2018

International Journal of Differential Equations

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This paper is concerned with the existence of asymptotically almost automorphic mild solutions to a class of abstract semilinear fractional differential equations D ( ) = ( ) + D −1 ( , ( ), ( )), ∈ R, where 1 < < 2, is a linear densely defined operator of sectorial type on a complex Banach space and is a bounded linear operator defined on , is an appropriate function defined on phase space, and the fractional derivative is understood in the Riemann-Liouville sense. Combining the fixed point theorem due to Krasnoselskii and a decomposition technique, we prove the existence of asymptotically almost automorphic mild solutions to such problems. Our results generalize and improve some previous results since the (locally) Lipschitz continuity on the nonlinearity is not required. The results obtained are utilized to study the existence of asymptotically almost automorphic mild solutions to a fractional relaxation-oscillation equation.

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Section: International Journal Of Differential Equationsmentioning

confidence: 99%

Section: International Journal Of Differential Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Existence of Asymptotically Almost Automorphic Mild Solutions of Semilinear Fractional Differential Equations

Cao

Huang²,

N’Guérékata

2018

International Journal of Differential Equations

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“…In recent years, there has been a significant development in fractional differential equations. One can see the monographs of Kilbas et al [18], Miller et al [24], Podlubny [29], Lakshmikantham et al [19], and the papers [7,10,11,17,20,21,27,28] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A class of nonlocal integrodifferential equations via fractional derivative and its mild solutions

Wang¹,

Yan²,

Zhang³

et al. 2011

OpMath

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Abstract. In this paper, we discuss a class of integrodifferential equations with nonlocal conditions via a fractional derivative of the type:Some sufficient conditions for the existence of mild solutions for the above system are given. The main tools are the resolvent operators and fixed point theorems due to Banach's fixed point theorem, Krasnoselskii's fixed point theorem and Schaefer's fixed point theorem. At last, an example is given for demonstration.

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“…As shown in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references therein, differential equations with delay or differential equations of fractional order have appeared in many branches of science and technology. They have received a lot of attention in all these years.…”

Section: Introductionmentioning

confidence: 99%

Mild Solutions to the Cauchy Problem for Some Fractional Differential Equations with Delay

Liang

2017

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Abstract:In this paper, we present new existence theorems of mild solutions to Cauchy problem for some fractional differential equations with delay. Our main tools to obtain our results are the theory of analytic semigroups and compact semigroups, the Kuratowski measure of non-compactness, and fixed point theorems, with the help of some estimations. Examples are also given to illustrate the applicability of our results.

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Weighted pseudo almost automorphic mild solutions to semilinear fractional differential equations

Cited by 33 publications

References 31 publications

Existence of Asymptotically Almost Automorphic Mild Solutions of Semilinear Fractional Differential Equations

Existence of Asymptotically Almost Automorphic Mild Solutions of Semilinear Fractional Differential Equations

A class of nonlocal integrodifferential equations via fractional derivative and its mild solutions

Mild Solutions to the Cauchy Problem for Some Fractional Differential Equations with Delay

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