Fractional representation formulae and right fractional inequalities
نویسنده
چکیده
Here we prove fractional representation formulae involving generalized fractional derivatives, Caputo fractional derivatives and Riemann–Liouville fractional derivatives. Then we establish Poincaré, Sobolev, Hilbert–Pachpatte and Opial type fractional inequalities, involving the right versions of the abovementioned fractional derivatives.
منابع مشابه
Multivariate weighted Fractional Representation Formulae and Ostrowski type inequalities
Here we derive multivariate weighted fractional representation formulae involving ordinary partial derivatives of rst order. Then we present related multivariate weighted fractional Ostrowski type inequalities with respect to uniform norm. 2010 AMS Mathematics Subject Classi cation : 26A33, 26D10, 26D15.
متن کاملOn Hadamard and Fej'{e}r-Hadamard inequalities for Caputo $small{k}$-fractional derivatives
In this paper we will prove certain Hadamard and Fejer-Hadamard inequalities for the functions whose nth derivatives are convex by using Caputo k-fractional derivatives. These results have some relationship with inequalities for Caputo fractional derivatives.
متن کاملOn Generalizations of Hadamard Inequalities for Fractional Integrals
Fej'{e}r Hadamard inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r Hadamard inequalities for $k$-fractional integrals. We deduce Fej'{e}r Hadamard-type inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.
متن کاملNabla discrete fractional calculus and nabla inequalities
Here we define a Caputo like discrete nabla fractional difference and we produce discrete nabla fractional Taylor formulae for the first time. We estimate their remaiders. Then we derive related discrete nabla fractional Opial, Ostrowski, Poincaré and Sobolev type inequalities .
متن کاملNew classes of Lyapunov type inequalities of fractional $Delta$-difference Sturm-Liouville problems with applications
In this paper, we consider a new study about fractional $Delta$-difference equations. We consider two special classes of Sturm-Liouville problems equipped with fractional $Delta$-difference operators. In couple of steps, the Lyapunov type inequalities for both classes will be obtained. As application, some qualitative behaviour of mentioned fractional problems such as stability, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Mathematical and Computer Modelling
دوره 54 شماره
صفحات -
تاریخ انتشار 2011