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Volumen 3 (2017): Heft 1 (June 2017)

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Volumen 1 (2015): Heft 1 (June 2015)

Zeitschriftendaten
Format
Zeitschrift
eISSN
2351-8227
Erstveröffentlichung
16 Apr 2015
Erscheinungsweise
3 Hefte pro Jahr
Sprachen
Englisch

Suche

Volumen 3 (2017): Heft 1 (June 2017)

Zeitschriftendaten
Format
Zeitschrift
eISSN
2351-8227
Erstveröffentlichung
16 Apr 2015
Erscheinungsweise
3 Hefte pro Jahr
Sprachen
Englisch

Suche

10 Artikel
Uneingeschränkter Zugang

Global Well-Posedness for Fractional Navier-Stokes Equations in critical Fourier-Besov-Morrey Spaces

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 1 - 13

Zusammenfassung

Abstract

In this paper we study the Cauchy problem of the Fractional Navier-Stokes equations in critical Fourier-Besov-Morrey spaces FṄsp, λ,q(ℝ3) with . By making use of the Fourier localization method and the Littlewood-Paley theory as in [6] and [21], we get global well-posedness result with small initial data belonging to . The space FṄsp,λ,q(ℝ3) covers the classical spaces Ḃsq and FḂsp,q(ℝ3) (cf [7],[3], [19], [22]...). The result of this paper extends the works of [6] and [21].

Schlüsselwörter

  • Navier-Stokes Equations
  • global well-posedness
  • Fourier-Besov- Morrey space
Uneingeschränkter Zugang

Hermite-Hadamard Type Inequalities for (α, m)- Convex Functions via Fractional Integrals

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 15 - 21

Zusammenfassung

Abstract

In this paper, we establish Hermite-Hadamard type inequalities for (α, m)-convex functions via fractional integrals.

Schlüsselwörter

  • Hadamard inequality
  • m)-convex function
  • m-convex function
  • Hölder inequality
  • Riemann-Liouville fractional integral
Uneingeschränkter Zugang

Hermite-Hadamard type inequalities for p-convex functions via fractional integrals

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 22 - 34

Zusammenfassung

Abstract

In this paper, we present Hermite-Hadamard inequality for p-convex functions in fractional integral forms. we obtain an integral equality and some Hermite-Hadamard type integral inequalities for p-convex functions in fractional integral forms. We give some Hermite-Hadamard type inequalities for convex, harmonically convex and p-convex functions. Some results presented in this paper for p-convex functions, provide extensions of others given in earlier works for convex, harmonically convex and p-convex functions.

Schlüsselwörter

  • Hermite-Hadamard inequalities,fractional integral
  • convex functions
  • harmonically convex functions
  • p-convex functions
Uneingeschränkter Zugang

Stability via successive approximation for nonlinear implicit fractional differential equations

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 36 - 54

Zusammenfassung

Abstract

In this paper we are concerned with nonlinear implicit fractional differential equations with initial conditions. We prove the existence and uniqueness results by using modified version of contraction principle. Further, our prime aim is to present various Ulam-Hyers stability and Eα-Ulam-Hyers stability results via successive approximation method.

Schlüsselwörter

  • Implicit fractional differential equation
  • Modified version of contraction principle
  • Existence
  • Ulam-Hyers Stability
  • Successive approximations
Uneingeschränkter Zugang

m-Convexity and Functional Equations

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 56 - 62

Zusammenfassung

Abstract

In this research we aim to explore some properties of m-convex functions from the point of view of functional equations or better, functional inequalities. So far studies of m- convexity have been devoted mainly to establish properties, inequalities and examples on the topic, but not to look at the problem from the perspective of functional inequalities.

Schlüsselwörter

  • Implicit fractional differential equation
  • Modified version of contraction principle
  • Existence
  • Ulam-Hyers Stability
  • Successive approximations
Uneingeschränkter Zugang

Inequalities for the m-th derivative of the (q; k)-Gamma function

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 63 - 68

Zusammenfassung

Abstract

By using the generalized Hölder’s and Minkowski’s integral inequalities, some inequalities for the m-th derivative of the (q; k)-Gamma function are established. Consequently, some previous results are recovered as particular cases of the present results.

Schlüsselwörter

  • Gamma function
  • (q
  • k)-analogue
  • inequality
Uneingeschränkter Zugang

Infinitely Many Solutions of the Neumann Problem for Elliptic systems in Anisotropic Variable Exponent Sobolev Spaces

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 70 - 82

Zusammenfassung

Abstract

In this paper, we prove the existence of in finitely many solutions for the following system by applying a critical point variational principle obtained by Ricceri as a consequence of a more general variational principle and the theory of the anisotropic variable exponent Sobolev spaces 2010 Mathematics Subject Classification. 35K05 - 35K55.

Schlüsselwörter

  • Neumann elliptic problem
  • Gradient system
  • weak solutions
  • Variational principle
  • Anisotropic variable exponent Sobolev spaces

MSC 2010

  • 35K05
  • 35K55
Uneingeschränkter Zugang

Inequalities of Hermite-Hadamard Type for HA-Convex Functions

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 83 - 101

Zusammenfassung

Abstract

Some new inequalities of Hermite-Hadamard type for HA-convex functions defined on positive intervals are given.

Schlüsselwörter

  • Convex functions
  • Integral inequalities
  • HA-Convex functions

MSC 2010

  • 26D15
  • 25D10
Uneingeschränkter Zugang

Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 102 - 115

Zusammenfassung

Abstract

In this paper, the notion of generalized (s; m; ξ)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized (s; m; ξ)-preinvex functions along with beta function are given. Moreover, we establish some new Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions via classical and Riemann-Liouville fractional integrals. These results not only extend the results appeared in the literature (see [10],[11]), but also provide new estimates on these types. At the end, some conclusions are given.

Schlüsselwörter

  • Hermite-Hadamard type inequality
  • Hölder’s inequality
  • power mean inequality
  • Young’s inequality
  • Riemann-Liouville fractional integral
  • s-convex in the second sense
  • m-invex
  • P-function

MSC 2010

  • Primary: 26A51
  • Secondary: 26D10
  • 26D15
Uneingeschränkter Zugang

Fractional parabolic problems with a nonlocal initial condition

Online veröffentlicht: 17 May 2018
Seitenbereich: 116 - 130

Zusammenfassung

Abstract

In this work we will consider a class of non local parabolic problems with nonlocal initial condition, more precisely we deal with the problem

where is a bounded domain, the function a can be a singular potential, g is a suitable function which will be specified later and p, θ Abstract. In this work we will consider a class of non local parabolic problems with nonlocal initial condition, more precisely we deal with the problem under natural conditions on the data. The question of global existence is also analyzed.

Schlüsselwörter

  • Fractional Laplacian parabolic problem
  • nonlocal initial condition
  • Hardy potential

MSC 2010

  • 35B25
  • 35K58
  • 35B33
  • 47G20
10 Artikel
Uneingeschränkter Zugang

Global Well-Posedness for Fractional Navier-Stokes Equations in critical Fourier-Besov-Morrey Spaces

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 1 - 13

Zusammenfassung

Abstract

In this paper we study the Cauchy problem of the Fractional Navier-Stokes equations in critical Fourier-Besov-Morrey spaces FṄsp, λ,q(ℝ3) with . By making use of the Fourier localization method and the Littlewood-Paley theory as in [6] and [21], we get global well-posedness result with small initial data belonging to . The space FṄsp,λ,q(ℝ3) covers the classical spaces Ḃsq and FḂsp,q(ℝ3) (cf [7],[3], [19], [22]...). The result of this paper extends the works of [6] and [21].

Schlüsselwörter

  • Navier-Stokes Equations
  • global well-posedness
  • Fourier-Besov- Morrey space
Uneingeschränkter Zugang

Hermite-Hadamard Type Inequalities for (α, m)- Convex Functions via Fractional Integrals

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 15 - 21

Zusammenfassung

Abstract

In this paper, we establish Hermite-Hadamard type inequalities for (α, m)-convex functions via fractional integrals.

Schlüsselwörter

  • Hadamard inequality
  • m)-convex function
  • m-convex function
  • Hölder inequality
  • Riemann-Liouville fractional integral
Uneingeschränkter Zugang

Hermite-Hadamard type inequalities for p-convex functions via fractional integrals

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 22 - 34

Zusammenfassung

Abstract

In this paper, we present Hermite-Hadamard inequality for p-convex functions in fractional integral forms. we obtain an integral equality and some Hermite-Hadamard type integral inequalities for p-convex functions in fractional integral forms. We give some Hermite-Hadamard type inequalities for convex, harmonically convex and p-convex functions. Some results presented in this paper for p-convex functions, provide extensions of others given in earlier works for convex, harmonically convex and p-convex functions.

Schlüsselwörter

  • Hermite-Hadamard inequalities,fractional integral
  • convex functions
  • harmonically convex functions
  • p-convex functions
Uneingeschränkter Zugang

Stability via successive approximation for nonlinear implicit fractional differential equations

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 36 - 54

Zusammenfassung

Abstract

In this paper we are concerned with nonlinear implicit fractional differential equations with initial conditions. We prove the existence and uniqueness results by using modified version of contraction principle. Further, our prime aim is to present various Ulam-Hyers stability and Eα-Ulam-Hyers stability results via successive approximation method.

Schlüsselwörter

  • Implicit fractional differential equation
  • Modified version of contraction principle
  • Existence
  • Ulam-Hyers Stability
  • Successive approximations
Uneingeschränkter Zugang

m-Convexity and Functional Equations

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 56 - 62

Zusammenfassung

Abstract

In this research we aim to explore some properties of m-convex functions from the point of view of functional equations or better, functional inequalities. So far studies of m- convexity have been devoted mainly to establish properties, inequalities and examples on the topic, but not to look at the problem from the perspective of functional inequalities.

Schlüsselwörter

  • Implicit fractional differential equation
  • Modified version of contraction principle
  • Existence
  • Ulam-Hyers Stability
  • Successive approximations
Uneingeschränkter Zugang

Inequalities for the m-th derivative of the (q; k)-Gamma function

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 63 - 68

Zusammenfassung

Abstract

By using the generalized Hölder’s and Minkowski’s integral inequalities, some inequalities for the m-th derivative of the (q; k)-Gamma function are established. Consequently, some previous results are recovered as particular cases of the present results.

Schlüsselwörter

  • Gamma function
  • (q
  • k)-analogue
  • inequality
Uneingeschränkter Zugang

Infinitely Many Solutions of the Neumann Problem for Elliptic systems in Anisotropic Variable Exponent Sobolev Spaces

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 70 - 82

Zusammenfassung

Abstract

In this paper, we prove the existence of in finitely many solutions for the following system by applying a critical point variational principle obtained by Ricceri as a consequence of a more general variational principle and the theory of the anisotropic variable exponent Sobolev spaces 2010 Mathematics Subject Classification. 35K05 - 35K55.

Schlüsselwörter

  • Neumann elliptic problem
  • Gradient system
  • weak solutions
  • Variational principle
  • Anisotropic variable exponent Sobolev spaces

MSC 2010

  • 35K05
  • 35K55
Uneingeschränkter Zugang

Inequalities of Hermite-Hadamard Type for HA-Convex Functions

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 83 - 101

Zusammenfassung

Abstract

Some new inequalities of Hermite-Hadamard type for HA-convex functions defined on positive intervals are given.

Schlüsselwörter

  • Convex functions
  • Integral inequalities
  • HA-Convex functions

MSC 2010

  • 26D15
  • 25D10
Uneingeschränkter Zugang

Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions

Online veröffentlicht: 01 Aug 2017
Seitenbereich: 102 - 115

Zusammenfassung

Abstract

In this paper, the notion of generalized (s; m; ξ)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized (s; m; ξ)-preinvex functions along with beta function are given. Moreover, we establish some new Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions via classical and Riemann-Liouville fractional integrals. These results not only extend the results appeared in the literature (see [10],[11]), but also provide new estimates on these types. At the end, some conclusions are given.

Schlüsselwörter

  • Hermite-Hadamard type inequality
  • Hölder’s inequality
  • power mean inequality
  • Young’s inequality
  • Riemann-Liouville fractional integral
  • s-convex in the second sense
  • m-invex
  • P-function

MSC 2010

  • Primary: 26A51
  • Secondary: 26D10
  • 26D15
Uneingeschränkter Zugang

Fractional parabolic problems with a nonlocal initial condition

Online veröffentlicht: 17 May 2018
Seitenbereich: 116 - 130

Zusammenfassung

Abstract

In this work we will consider a class of non local parabolic problems with nonlocal initial condition, more precisely we deal with the problem

where is a bounded domain, the function a can be a singular potential, g is a suitable function which will be specified later and p, θ Abstract. In this work we will consider a class of non local parabolic problems with nonlocal initial condition, more precisely we deal with the problem under natural conditions on the data. The question of global existence is also analyzed.

Schlüsselwörter

  • Fractional Laplacian parabolic problem
  • nonlocal initial condition
  • Hardy potential

MSC 2010

  • 35B25
  • 35K58
  • 35B33
  • 47G20

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