Fractional calculus for interval-valued functions

Lupulescu, Vasile

doi:10.1016/j.fss.2014.04.005

Cited by 184 publications

(79 citation statements)

References 50 publications

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“…In fact, operator It has good properties, such as (more details ones can refer to c.f. [28] thus is,…”

Section: Fractional Calculus For Interval-valued Functions and Partiamentioning

confidence: 97%

Existence of solutions for fractional interval--valued differential equations by the method of upper and lower solutions

Huang¹,

Bai²,

Liu³

et al. 2017

MMN

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Abstract. In this work we firstly study some important properties of fractional calculus for interval-valued functions and introduce the concepts of upper and lower solutions for intervalvalued Caputo fractional differential equations. Then, we prove an existence result for intervalvalued Caputo fractional differential equations by use of the method of upper and lower solutions. Finally several examples will be presented to illustrate our abstract results.

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“…In fact, operator It has good properties, such as (more details ones can refer to c.f. [28] thus is,…”

Section: Fractional Calculus For Interval-valued Functions and Partiamentioning

confidence: 97%

Existence of solutions for fractional interval--valued differential equations by the method of upper and lower solutions

Huang¹,

Bai²,

Liu³

et al. 2017

MMN

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“…This includes the functions' derivative of arbitrary order. The topic has been explored and studied by various researchers in many fields such as engineering, mathematics and so forth [2,14,15,17,22,33,35]. One of the major contributions in this field was the work in [37], which discussed the topic intensively.…”

Section: Introductionmentioning

confidence: 99%

Solving fuzzy fractional differential equations using fuzzy Sumudu transform

Rahman¹,

Ahmad²

2017

J. Nonlinear Sci. Appl.

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“…We can refer to papers [11,12,13,14,15] etc. Boundary value problems for FFDEs, which are the combination of fuzzy analysis and boundary value problems for fractional differential equations, are a very magical and practical field.…”

Section: Introductionmentioning

confidence: 99%

Existence of Solutions to Boundary Value Problems for a Class of Nonlinear Fuzzy Fractional Differential Equations

Wang¹,

Sun²,

Han³

2017

AAN

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In this paper, we investigate the existence and uniqueness of solution to boundary value problems for a class of nonlinear fuzzy factional differential equations involving the fuzzy gHfractional Caputo derivative. By means of the Schauder fixed point theorem in semi-linear spaces and integral inequality technique, some qualitative results of solutions are obtained. An example is provided from which new results are found.

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Fractional calculus for interval-valued functions

Cited by 184 publications

References 50 publications

Existence of solutions for fractional interval--valued differential equations by the method of upper and lower solutions

Existence of solutions for fractional interval--valued differential equations by the method of upper and lower solutions

Solving fuzzy fractional differential equations using fuzzy Sumudu transform

Existence of Solutions to Boundary Value Problems for a Class of Nonlinear Fuzzy Fractional Differential Equations

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