A difference equation is a relation between the differences of a function at one or more general values of the independent variable. These equations usually describe the evolution of certain phenomena over the course of time. The present paper deals with the existence and uniqueness of solutions of fractional difference equations.
Abstract. In this paper some discrete Opial type inequalities of fractional order are established and using these inequalities of Opial type, a bound to the solution of a fractional initial value problem is obtained.Mathematics subject classification (2010): 39A10, 39A99.
The impact of heat and mass transfer effects on an MHD flow past an inclined porous plate in the presence of a chemical reaction is investigated in this study. An effort has been made to explain the Soret effect and the influence of an angle of inclination on the flow field, in the presence of the heat source, chemical reaction and thermal radiation. The momentum, energy and concentration equations are derived as coupled second order partial differential equations. The model is non-dimensionalized and shown to be controlled by a number of dimensionless parameters. The resulting dimensionless partial differential equations can be solved by using a closed analytical method. Numerical results for pertaining parameters, such as the Soret number (Sr), Grashof number (Gr) for heat and mass transfer, the Schmidt number (Sc), Prandtl number (Pr), chemical reaction parameter (Kr), permeability parameter (K), magnetic parameter (M), skin friction (τ), Nusselt number (Nu) and Sherwood number (Sh) on the velocity, temperature and concentration profiles are presented graphically and discussed qualitatively.
The finite non-commutative and non-associative algebraic structures are indeed one of the special structures for their probabilistic results in some branches of mathematics. For a given integer n ≥ 2 , the nth-commutativity degree of a finite algebraic structure S, denoted by P n (S) , is the probability that for chosen randomly two elements x and y of S, the relator x n y = yx n holds. This degree is specially a recognition tool in identifying such structures and studied for associative algebraic structures during the years. In this paper, we study the nth-commutativity degree of two infinite classes of finite loops, which are non-commutative and non-associative. Also by deriving explicit expressions for nth-commutativity degree of these loops, we will obtain best upper bounds for this probability.
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