In this paper, we introduce and study a convoluted version of the time fractional Poisson process by taking discrete convolution with respect to space variable in system differential equations that governs its state probabilities. We call introduced as (CFPP). The explicit expression for Laplace transform probabilities are obtained whose inversion yields one-dimensional distribution. Some stati...

To study the short-term uptake of potassium across the basolateral membrane into individual tubule cells, rubidium was used and measured by electron microprobe analysis. Changes of rubidium uptake were interpreted to reflect altered sodium entry and basolateral Na-K-ATPase activity. The effects of hydrochlorothiazide, amiloride and furosemide were determined in saline-loaded animals. Hydrochlor...

The distal convoluted tubule is the nephron segment that lies immediately downstream of the macula densa. Although short in length, the distal convoluted tubule plays a critical role in sodium, potassium, and divalent cation homeostasis. Recent genetic and physiologic studies have greatly expanded our understanding of how the distal convoluted tubule regulates these processes at the molecular l...

The Inversion Problem Our standard modeling and control concepts and techniques include linear convolution models and various transform techniques (the Laplace transform, the Z-transform, the bilateral Laplace transform, the bilateral Z-transform, the continuous Fourier transform, and the discrete Fourier transform). In fact, these techniques form the basis of the broad areas of circuits, commu...

Convoluted C-cosine functions and semigroups in a Banach space setting extending the classes of fractionally integrated C-cosine functions and semigroups are systematically analyzed. Structural properties of such operator families are obtained. Relations between convoluted C-cosine functions and analytic convoluted C-semigroups, introduced and investigated in this paper are given through the co...