Generalized Extended Riemann-Liouville Type Fractional Derivative Operator

نویسندگان

چکیده

In this paper, we present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella functions, by using the extended Bessel due to Boudjelkha [?]. Some recurrence relations, transformation formulas, Mellin transform integral representations are obtained for these generalizations. Further, an extension Riemann-Liouville fractional derivative operator is established.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Fractional Ince equation with a Riemann-Liouville fractional derivative

We extend the classical treatment of the Ince equation to include the effect of a fractional derivative term of order a > 0 and amplitude c. A Fourier expansion is used to determine the eigenvalue curves að Þ in function of the parameter , the stability domains, and the periodic stable solutions of the fractional Ince equation. Two important observations are the detachment of the eigenvalue cur...

متن کامل

Space-Time Fractional Reaction-Diffusion Equations Associated with a Generalized Riemann-Liouville Fractional Derivative

This paper deals with the investigation of the computational solutions of a unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann–Liouville fractional derivative defined by others and the space derivative of second order by the Riesz–Feller fractional derivative and adding...

متن کامل

Riemann-Liouville integrals of fractional order and extended KP hierarchy

An attempt is given to formulate the extensions of the KP hierarchy by introducing fractional order pseudo-differential operators. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered he...

متن کامل

ON GENERALIZED k-FRACTIONAL DERIVATIVE OPERATOR

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to khypergeometric and k-Appell’s functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

متن کامل

Some new Hardy-type inequalities for Riemann-Liouville fractional q-integral operator

*Correspondence: [email protected] 1Luleå University of Technology, Luleå, 971 87, Sweden 2Narvik University College, P.O. Box 385, Narvik, 8505, Norway Full list of author information is available at the end of the article Abstract We consider the q-analog of the Riemann-Liouville fractional q-integral operator of order n ∈ N. Some new Hardy-type inequalities for this operator are proved and dis...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Kragujevac journal of mathematics

سال: 2023

ISSN: ['2406-3045', '1450-9628']

DOI: https://doi.org/10.46793/kgjmat2301.057a