A Review of the Assessment Methods of Voice Disorders in the Context of Parkinson's Disease

In recent years, a significant progress in the field of research dedicated to the treatment of disabilities has been witnessed. This is particularly true for neurological diseases, which generally influence the system that controls the execution of learned motor patterns. In addition to its importance for communication with the outside world and interaction with others, the voice is a reflection of our personality, moods and emotions. It is a way to provide information on health status, shape, intentions, age and even the social environment. It is also a working tool for many, but an important element of life for all. Patients with Parkinson’s disease (PD) are numerous and they suffer from hypokinetic dysarthria, which is manifested in all aspects of speech production: respiration, phonation, articulation, nasalization and prosody. This paper provides a review of the methods of the assessment of speech disorders in the context of PD and also discusses the limitations

Novel Numerical Investigations of Fuzzy Cauchy Reaction–Diffusion Models via Generalized Fuzzy Fractional Derivative Operators

The present research correlates with a fuzzy hybrid approach merged with a homotopy perturbation transform method known as the fuzzy Shehu homotopy perturbation transform method (SHPTM). With the aid of Caputo and Atangana–Baleanu under generalized Hukuhara differentiability, we illustrate the reliability of this scheme by obtaining fuzzy fractional Cauchy reaction–diffusion equations (CRDEs) with fuzzy initial conditions (ICs). Fractional CRDEs play a vital role in diffusion and instabilities may develop spatial phenomena such as pattern formation. By considering the fuzzy set theory, the proposed method enables the solution of the fuzzy linear CRDEs to be evaluated as a series of expressions in which the components can be efficiently identified and generating a pair of approximate solutions with the uncertainty parameter λ∈[0,1]. To demonstrate the usefulness and capabilities of the suggested methodology, several numerical examples are examined to validate convergence outcomes for the supplied problem. The simulation results reveal that the fuzzy SHPTM is a viable strategy for precisely and accurately analyzing the behavior of a proposed model

Novel Numerical Investigations of Fuzzy Cauchy Reaction–Diffusion Models via Generalized Fuzzy Fractional Derivative Operators

The present research correlates with a fuzzy hybrid approach merged with a homotopy perturbation transform method known as the fuzzy Shehu homotopy perturbation transform method (SHPTM). With the aid of Caputo and Atangana–Baleanu under generalized Hukuhara differentiability, we illustrate the reliability of this scheme by obtaining fuzzy fractional Cauchy reaction–diffusion equations (CRDEs) with fuzzy initial conditions (ICs). Fractional CRDEs play a vital role in diffusion and instabilities may develop spatial phenomena such as pattern formation. By considering the fuzzy set theory, the proposed method enables the solution of the fuzzy linear CRDEs to be evaluated as a series of expressions in which the components can be efficiently identified and generating a pair of approximate solutions with the uncertainty parameter λ∈[0,1]. To demonstrate the usefulness and capabilities of the suggested methodology, several numerical examples are examined to validate convergence outcomes for the supplied problem. The simulation results reveal that the fuzzy SHPTM is a viable strategy for precisely and accurately analyzing the behavior of a proposed model

Numerical treatment of first order delay differential equations using extended block backward differentiation formulae

In this research, we developed and implemented extended backward differentiation methods (formulae) in block forms for step numbers k = 2, 3 and 4 to evaluate numerical solutions for certain first-order differential equations of delay type, generally referred to as delay differential equations (DDEs), without the use of interpolation methods for estimating the delay term. The matrix inversion approach was applied to formulate the continuous composition of these block methods through linear multistep collocation method. The discrete schemes were established through the continuous composition for each step number, which evaluated the error constants, order, consistency, convergent and area of absolute equilibrium of these discrete schemes. The study of the absolute error results revealed that, as opposed to the exact solutions, the lower step number implemented with super futures points work better than the higher step numbers implemented with super future points