نتایج جستجو برای: liouville fractional integral

تعداد نتایج: 176113  

Journal: :international journal of mathematical modelling and computations 0
y. ordokhani department of applied mathematics, faculty of mathematical sciences, alzahra university, tehran, iran. n. rahimi department of applied mathematics, faculty of mathematical sciences, alzahra university, tehran, iran.

abstract. in this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized haar functions. for this purpose, the properties of hybrid of rationalized haar functions are presented. in addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...

Journal: :sahand communications in mathematical analysis 0
somayeh nemati department of mathematics, faculty of mathematical sciences, university of mazandaran, babolsar, iran.

in this paper, we consider the second-kind chebyshev polynomials (skcps) for the numerical solution of the fractional optimal control problems (focps). firstly, an introduction of the fractional calculus and properties of the shifted skcps are given and then operational matrix of fractional integration is introduced. next, these properties are used together with the legendre-gauss quadrature fo...

2015
Yusong Lu Wu-Sheng Wang Hua Zhong

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...

Journal: :bulletin of the iranian mathematical society 0
m. behroozifar department of mathematics‎, ‎faculty of basic sciences‎, ‎babol noshirvani university of technology‎, ‎babol‎, ‎mazandaran‎, ‎iran. f. ahmadpour department of mathematics‎, ‎faculty of basic sciences‎, ‎babol noshirvani university of technology‎, ‎babol‎, ‎mazandaran‎, ‎iran.

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

2016
SOTIRIS K. NTOUYAS PRAVEEN AGARWAL JESSADA TARIBOON S. K. NTOUYAS P. AGARWAL J. TARIBOON

In this paper, we investigate some new Pólya-Szegö type integral inequalities involving the Riemann-Liouville fractional integral operator, and use them to prove some fractional integral inequalities of Chebyshev type, concerning the integral of the product of two functions and the product of two integrals. Certain special cases are also considered. Finally, examples for constructing the boundi...

Journal: :computational methods for differential equations 0
amjad ali university of malakand kamal shah university of malakand rahmat ali khan department of mathematics university of malakand

this paper is devoted to the study of establishing sufficient conditions forexistence and uniqueness of positive solution to a class ofnon-linear problems of fractional differential equations. the boundary conditionsinvolved riemann-liouville fractional order derivative and integral. further, the non-linear function $f$ containfractional order derivative which produce extra complexity. thank to...

2017
Erhan Set Muhammed Aslam Noor Muhammed Uzair Awan Abdurrahman Gözpinar

In this article, a new general integral identity involving generalized fractional integral operators is established. With the help of this identity new Hermite-Hadamard type inequalities are obtained for functions whose absolute values of derivatives are convex. As a consequence, the main results of this paper generalize the existing Hermite-Hadamard type inequalities involving the Riemann-Liou...

This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...

E. Babolian, P. Rahimkhani, Y. Ordokhani,

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....

Journal: :CoRR 2002
W. Chen

The fractional Laplacian and the fractional derivative are two different mathematical concepts (Samko et al, 1987). Both are defined through a singular convolution integral, but the former is guaranteed to be the positive definition via the Riesz potential as the standard Laplace operator, while the latter via the Riemann-Liouville integral is not. It is noted that the fractional Laplacian can ...

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