Aging and rejuvenation with fractional derivatives

Mitochondria are eukaryotic cellular organelles that are known to produce energy through a process called oxidative phosphorylation. Besides their primary function, mitochondria are involved in various cellular processes, including cell growth, differentiation, signaling, metabolism, and senescence. Age-related changes cause a decline in mitochondrial quality and integrity due to increased mitochondrial mutations and oxidative damage. Thus, aging can severely impact mitochondrial functions,...

The skin is divided into epidermis, dermis, and hypodermis, the skin's outermost, middle, and inner layers. The human epidermal layer regularly undergoes renewal, where old, dead cells are replaced by new cells. Epidermal stem cells or EpiSCs divide and differentiate to restore the lost cells. For the renewal process, some EpiSCs continuously self-renew. In contrast, few others differentiate into transit-amplifying cells, which later form prickle or spinous cells, followed by granular cells,...

Several body functions deteriorate with age. The external signs of aging are easily identifiable. For example, the skin becomes dry, less elastic, and thins out, forming wrinkles. The skin of the face begins to appear looser due to a decrease in the levels of elastic and collagen fibers in the connective tissue. Additionally, melanin production in the hair follicle decreases with age, resulting in gray hair. Moreover, the senses of sight and hearing decline, so glasses and hearing aids may...

Aging is a complex biological phenomenon influenced by various processes that affect cellular and systemic functions. Several prominent theories attempt to explain its mechanisms, highlighting cellular limitations, oxidative damage, and hormonal changes as central factors in aging.
Cellular Clock Theory
The cellular clock theory posits that the human lifespan is closely tied to the finite capacity of cells to divide, a phenomenon governed by telomeres, which are protective caps at the ends of...

DerivativesThe concept of instantaneous rate of change is fundamental in both mathematics and physics, particularly in describing how a moving object alters its position with respect to time. This rate is captured mathematically through the derivative of a function. The derivative at a point represents the slope of the tangent line to the curve of the function at that point and quantifies how the function’s output changes per infinitesimal change in input.Derivative of the Square Root...

In calculus, higher-order derivatives extend the idea of differentiation beyond the first derivative to capture successive rates of change. These derivatives provide detailed information about the behavior of functions and have important applications in both mathematics and physics. To illustrate these concepts, consider the example function\begin{equation*}f(x) = x^3 - x\end{equation*}which serves as a useful case study for exploring higher derivatives.The first derivative represents the slope...