In this paper, we suggest the modified Extended Direct Algebraic Method (mEDAM) to examine the existence and dynamics of solitary wave solutions in the context of the fractional coupled Higgs system, with Caputo’s fractional derivatives. The method begins with the formulation of nonlinear differential equations using a fractional complex transformation, followed by the derivation of solitary wave solutions. Two-dimensional, Three-dimensional and contour graphs are used to investigate the behavior of traveling wave solutions. The research reveals many families of solitary wave solutions as well as their deep interrelationships and dynamics. These discoveries add to a better understanding of the dynamics of the fractionally coupled Higgs system and have potential applications in areas that use nonlinear Fractional Partial Differential Equations (FPDEs).

This study generates and investigates spreading solitons in the fractional DR quadratic equation (FDE) with fractional derivatives using the Extended Direct Algebraic Method (EDAM). In population growth, mathematical biology, and reaction-diffusion mechanisms, the FDE is crucial. Applying the series form solution to the NODE from the FDE conversion into a recommended EDAM yields many traveling soliton solutions. To characterize and explore soliton structure propagation, we draw shock and kink soliton solutions. Through reaction-diffusion mechanics and mathematical biology, we may explain complex processes in many academic subjects.

This work studies the space-time fractional modified Benjamin-Bona-Mahony equation, a mathematical model of nonlinear wave propagation in various physical systems, for solitary wave solutions. Among the precise solutions we produce with the Extended Direct Algebraic method are solitary waves and periodic wave patterns. These solutions reveal information on soliton interactions and propagation processes, offering insight into the dynamics of the problem. Characterizing the answers is made easier with the use of graphic representations. Our work bridges the gap between chemical reaction-diffusion mechanisms and biological mathematics to improve comprehension of complicated events in interdisciplinary study.

HCV is the leading cause of liver related morbidity and mortality around the world. Chronic infection usually leads to serious outcomes like cirrhosis, hepatocellular carcinoma and metabolic abnormalities. Inability of HCV to replicate in cell culture and absence of efficient and cost effective animal models are the major hurdles in developing therpeutic strategies against this virus. Cloning and expression of HCV entire structural genome in eukaryotic expression system was observed in the current study. Structural genes of HCV are important in mediating viral entry in the host cell and pathogenesis, most notably hepatocellular carcinoma. HCV 3a is the most prevalent genotype in Pakistan. RNA was extracted from HCV positive serum infected with 3a genotype, and entire structural genome (C-E2) was reverse transcribed. HCV (C-E2) region was amplified using PCR with gene specific primers having restriction sites. Digested product of this amplicon was cloned in mammalian expression vector pcDNA3.1+. Positive clones were confirmed after double restriction digetsion and sequencing PCR. This successful clone of (C-E2) would be a useful tool for transfection to particular cell lines and further investigation on stable cell lines using this clone may help in designing new therapies and studying interaction of viral proteins with host cells.