Alzheimer’s Disease (AD), affecting a large population worldwide is characterized by the loss of memory and learning ability in the old population. The enzyme Acetylcholinesterase Enzyme (AChE) is the key enzyme in the hydrolysis of the neurotransmitter acetylcholine and is also the target of most of the clinically used drugs for the treatment of AD but these drugs provide only symptomatic treatment and have the limitation of loss of therapeutic efficacy with time. The development of different strategies targeting the AChE enzyme along with other targets like Butyl Cholinesterase (BChE), amyloid-β (Aβ), β-secretase-1 (BACE), metals antioxidant properties and free radical scavenging capacity has been focused in recent years. Literature search was conducted for the molecules and their rational design which have shown inhibition for AChE and the other abovementioned targets. Several hybrid molecules incorporating the main sub-structures derived from diverse chemotypes like acridine, quinoline, carbamates, and other heterocyclic analogs have shown desired pharmacological activity with a good profile in a single molecule. It is followed by optimization of the activity through structural modifications guided by structure-activity relationship studies. It has led to the discovery of novel molecules 17b, 20, and 23 with desired AChE inhibition along with desirable activity against other abovementioned targets for further pre-clinical studies.

Diabetes is a worldwide problem that affects one of every 11 persons nowadays. The IDF Diabetes Atlas (Eighth edition, 2017) states that approximately 415 million people in the world are living with the disease and that this number will rise to 629 million by the year 2045. It is a very serious problem of the world. A major part of the world population is affected by this disease and its resulting complications. In this paper, we propose to investigate a fractional-order model of diabetes and its resulting complications. The mathematical model's parameters define the population of diabetic patients and those who are diabetic with complications at a given time t. We have also discussed the existence, uniqueness, and stability of the fractional-order model, which we consider here. We make use of the homotopy decomposition method (HDM) in order to solve the problem. KEYWORDSdiabetes and its resulting complications, existence, fractional calculus, fractional-order modeling, homotopy decomposition method (HDM), uniqueness and stability

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An efficient approach based on homotopy perturbation method by using Sumudu transform is proposed to solve some linear and nonlinear space-time fractional Fokker-Planck equations (FPEs) in closed form. The space and time fractional derivatives are considered in Caputo sense. The homotopy perturbation Sumudu transform method (HPSTM) is a combined form of Sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. Some examples show that the HPSTM is an effective tool for solving many space time fractional partial differential equations.

Abstract:In the present paper, we use analytical techniques to solve fractional nonlinear differential equations systems that arise in Bergman's minimal model, used to describe blood glucose and insulin metabolism, after intravenous tolerance testing. We also discuss the stability and uniqueness of the solution.

In the present paper, we use an efficient approach to solve fractional differential equation, oxygen diffusion problem which is used to describe oxygen absorption in human body. The oxygen diffusion problem is considered in new Caputo derivative of fractional order in this paper. Using an iterative approach, we derive the solutions of the modified system. c 2017 all rights reserved.

Abstract. We discuss and derive the analytical solution for the generalized time-fractional telegraph equation. These problems are solved by taking the Laplace and Fourier transforms in variable t and x respectively. Here we use Green function also to derive the solution of the given differential equation.Mathematics subject classification (2010): Primary 26A33, 33C20, 33E12; secondary 47B38, 47G10.

In this paper, we solve the [Formula: see text]-Generalized KdV equation by local fractional homotopy analysis method (LFHAM). Further, we analyze the approximate solution in the form of non-differentiable generalized functions defined on Cantor sets. Some examples and special cases of the main results are also discussed.