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In this manuscript, the concept of ϝ-contraction is applied to extend the notion of Jaggi-Suzuki-type hybrid contraction in the framework of G-metric space, which is termed Jaggi-Suzukitype hybrid ϝ-(G-α-φ)-contraction, and invariant point results which cannot be inferred from their cognate ones in metric space are established. The results obtained herein provide a new direction and are generalizations of several well-known results in fixed point theory. An illustrative, comparative example is constructed to give credence to the results obtained. Furthermore, sufficient conditions for the existence and uniqueness of solutions of certain nonlinear polynomial and integral equations are established. For the purpose of future research, an open problem is highlighted regarding discretized population balance model whose solution may be investigated from the techniques proposed herein. [ABSTRACT FROM AUTHOR]

Fractional Differential inclusions, the multivalued version of fractional differential equations, yellow play a vital role in various fields of applied sciences. In the present article, a class of q-rung orthopair fuzzy (q-ROF) set valued mappings along with q-ROF upper/lower semi-continuity have been introduced. Based on these ideas, existence theorems for a numerical solution of a distinct class of fractional differential inclusions have been achieved with the help of Schaefer type and Banach contraction fixed point theorems. A physical example is also provided to validate the hypothesis of the main results. The notion of q-rung orthopair fuzzy mappings along with the use of fixed point techniques and a new-fangled Caputo type fractional derivative are the principal novelty of this article. [ABSTRACT FROM AUTHOR]

If G is a finite group and X a conjugacy class of elements of G, then we define rank(G: X) to be the minimum number of elements of X generating G. In the present article, we determine the ranks for the Fischer's simple group Fi'24 and the baby monster group B. [ABSTRACT FROM AUTHOR]

A group G is said to be (2,3,t)-generated if it can be generated by two elements x and y such that o(x) = 2, o(y) = 3 and o(xy) = t. In the present article, we investigate (2,3,t)-generations for the Held's sporadic simple group He, where t is a divisor of ∣He∣. Most of the computations were carried out with the aid of computer algebra system GAP [23]. [ABSTRACT FROM AUTHOR]