CHEBYSHEV TYPE INEQUALITIES FOR THE SAIGO FRACTIONAL INTEGRALS AND THEIR q–ANALOGUES

Sharp Inequalities for Functional Integrals and Traces of Conformally Invariant Operators

The intertwining operators Ad = Ad(g) on the round sphere (Sn, g) are the conformal analogues of the power Laplacians 1d/2 on the flat Rn . To each metric ρg, conformally equivalent to g, we can naturally associate an operator Ad(ρg), which is compact, elliptic, pseudodifferential of order d, and which has eigenvalues λ j (ρ); the special case d = 2 gives precisely the conformal Laplacian in th...

NEW CONNECTION FORMULAE BETWEEN (p, q)−FIBONACCI POLYNOMIALS AND CERTAIN JACOBI POLYNOMIALS

The main purpose of this article is to solve the connection problems between (p, q)−Fibonacci polynomials and the two polynomials, namely Chebyshev polynomials of third and fourth kinds which are considered as two nonsymmetric polynomials of the Jacobi polynomials. Moreover, the inversion connection formulae for the latter formulae are given. We show that all the connection coefficients are exp...

New inequalities for fractional integrals and their applications

The Stability of Non-standard Finite Difference Scheme for Solution of Partial Differential Equations of Fractional Order

Fractional derivatives and integrals are new concepts of derivatives and integrals of arbitrary order. Partial differential equations whose derivatives can be of fractional order are called fractional partial differential equations (FPDEs). Recently, these equations have received special attention due to their high practical applications. In this paper, we survey a rather general case of FPDE t...

Estimation of unknown function of a class of integral inequalities with pth power

Fractional differential equations and fractional integral equations have gained considerable importance and attention due to their applications in many engineering and scientific disciplines. Gronwall-Bellman inequalities are important tools in the study of existence, uniqueness, boundedness, stability and other qualitative properties of solutions of Fractional differential equations and fracti...