No abstract

We first define the $q$-analogue operators of fractional calculus which are then used in defining certain classes of functions analytic in the open disk. The results investigated for these classes of functions include the coefficient inequalities and some distortion theorems. The results provide extensions of various known results in the $q$-theory of analytic functions. Special cases of our results are pointed out briefly.

In this article, we develop a mathematical model considering susceptible, exposed, infected, asymptotic, quarantine/isolation and recovered classes as in case of COVID-19 disease. The facility of quarantine/isolation have been provided to both exposed and infected classes. Asymptotic individuals either recovered without undergo treatment or moved to infected class after some duration. We have formulated the reproduction number for the proposed model. Elasticity and sensitivity analysis indicates that model is more sensitive towards the transmission rate from exposed to infected classes rather than transmission rate from susceptible to exposed class. Analysis of global stability for the proposed model is studied through Lyapunov's function.

In this work, we aim to present a hybrid numerical scheme based on the homotopy analysis transform method (HATM) to examine the fractional model of nonlinear wave-like equations having variable coefficients, which narrate the evolution of stochastic systems. The wave-like equation models the erratic motions of small particles that are dipped in fluids and fluctuations of the stochastic behavior of exchange rates. The uniqueness and existence of HATM solution have also been discussed. Some numerical examples are given to establish the accurateness and effectiveness of the suggested scheme. Furthermore, we show that the proposed computational approach can give much better approximation than perturbation and Adomain decomposition method, which are the special cases of HATM. The result exhibits that the HATM is very productive, straight out and computationally very attractive.

Abstract. The aim of the present paper is to obtain certain new integral inequalities involving the Saigo fractional integral operator. It is also shown how the various inequalities considered in this paper admit themselves of q -extensions which are capable of yielding various results in the theory of q -integral inequalities.Mathematics subject classification (2010): 26D10, 26A33, 05A30.