Qualitative properties of difference equations

Abstract

newlineThis research focuses to develop and analyse the most significant and interesting topics of qualitative properties of solutions in certain class of difference-functional-equations. Active research is on since last few decades in analyzing the solutions of equations involving and#8710; but the study on the same property for difference equations involving and#8710;` and and#8710;and#945;(`) is rare. By employing the above mentioned operators, our aim is to obtain necessary conditions for the oscillation and non-oscillation of several class of difference equations based on the operators and#8710;, and#8710;` , and#8710;and#945;(`) and and#8710;q. Moreover, our findings are arrived by equating closed and summation form of solutions and they are verified with numerical values by MATLAB to measure its accuracy. In chapter 7, we discuss about the summation and exact type solutions for certain type of fractional order difference equation using multi-step delta operator and we also present suitable examples to illustrate our main results. In chapter 8, we discuss the generalized fractional proportional delta operator and new generalized transforms in discrete fractional calculus and the theory is well supported by presenting suitable examples