The forgotten topological index is defined as sum of third power of degrees. In this paper, we compute some properties of forgotten index and then we determine it for some classes of product graphs.

We consider the independent sum of a given random variable with a Gaussian variable and an infinitely divisible one. We find a novel tight upper bound on the entropy of the sum which still holds when the variable possibly has an infinite second moment. The proven bound has several implications on both information theoretic problems and infinitely divisible noise channels’ transmission rates.

In this paper, we study the variable-order (VO) time-fractional diffusion equations. For a VO function $$\alpha (t)\in (0,1)$$ , develop an exponential-sum-approximation (ESA) technique to approach Caputo fractional derivative. The ESA keeps both quadrature exponents and number of exponentials in summation unchanged at different time level. Approximating parameters are properly selected achieve...