On generalized composite fractional q-derivative

Le Matematiche

Lata Chanchlani¹  Mridula Garg²  Subhash Alha² 

[1] Department of Mathematics, S. S. Jain Subodh Girls College, Jaipur 302011, Rajasthan, India;Department of Mathematics, University of Rajasthan, Jaipur - 302004, Rajasthan, India;

关键词: q-Laplace transform;    q-integrals and q-derivatives;   

DOI  :  

来源: DOAJ

【 摘 要 】

In the present paper, we define a generalized composite fractional q-derivative D^{\alpha,\beta,\nu}_q and obtain some results for it. These results are image of power function under D^{\alpha,\beta,\nu}_q,  composition of Riemann-Liouville type fractional q-integral I^\alpha_q with D^{\alpha,\beta,\nu}_q  and q-Laplace transform of D^{\alpha,\beta,\nu}_q. We also obtain solution of a q-difference equation with derivative as D^{\alpha,\beta,\nu}_q  and discuss some special cases. A q-difference equation of D^{\alpha,\beta,\nu}_q  is solved using q-Laplace transform and its inverse.

【 授权许可】

Unknown