Caputo q-fractional initial value problems and a q-analogue Mittag–Leffler function
نویسندگان
چکیده
منابع مشابه
On q–fractional derivatives of Riemann–Liouville and Caputo type
Abstract. Based on the fractional q–integral with the parametric lower limit of integration, we define fractional q–derivative of Riemann–Liouville and Caputo type. The properties are studied separately as well as relations between them. Also, we discuss properties of compositions of these operators. Mathematics Subject Classification: 33D60, 26A33 .
متن کاملNontrivial solutions for fractional q-difference boundary value problems
In this paper, we investigate the existence of nontrivial solutions to the nonlinear q-fractional boundary value problem (D q y)(x) = −f(x, y(x)), 0 < x < 1, y(0) = 0 = y(1), by applying a fixed point theorem in cones.
متن کاملA distinct numerical approach for the solution of some kind of initial value problem involving nonlinear q-fractional differential equations
The fractional calculus deals with the generalization of integration and differentiation of integer order to those ones of any order. The q-fractional differential equation usually describe the physical process imposed on the time scale set Tq. In this paper, we first propose a difference formula for discretizing the fractional q-derivative of Caputo type with order and scale index . We es...
متن کاملA Mathematica q - Analogue
Mathematica implementations, available by email request, of q-analogues of Gosper's and Zeilberger's algorithm are described. Nontrivial examples are given in order to illustrate the usage of these packages. The algorithms are based on a new approach to q-hypergeometric telescoping in which a new algebraic concept, q-greatest factorial factorization (qGFF), plays a fundamental role.
متن کاملA q-analogue of ĝl3 hierarchy and q-Painlevé VI
A q-analogue of the ĝl3 Drinfel’d-Sokolov hierarchy is proposed as a reduction of the q-KP hierarchy. Applying a similarity reduction and a q-Laplace transformation to the hierarchy, one can obtain the q-Painlevé VI equation proposed by Jimbo and Sakai. AMS classification scheme numbers: 37K10, 39A12, 39A13 Submitted to: J. Phys. A: Math. Gen. Dedicated to Professors Junkichi Satsuma and Basil ...
متن کاملذخیره 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: Communications in Nonlinear Science and Numerical Simulation
سال: 2011
ISSN: 1007-5704
DOI: 10.1016/j.cnsns.2011.01.026