Fractional Differential Equations Involving the Spherical Bessel Function j0: Analytical Solutions Via Laplace Transform | Chapter 03 | Physical Science: New Insights and Developments Vol. 4

 

This work addresses the resolution of fractional differential equations whose nonhomogeneous part is given by the spherical Bessel function 𝐽₀(𝑥). By using the fractional derivative in the sense of Caputo and the Laplace transform, a general analytical solution is obtained in terms of the generalised hypergeometric functions 2^𝐹3, revealing a recurrent structure in the solutions. Furthermore, particular cases for integer and fractional orders are presented, highlighting the appearance of special functions such as the sine integral and Fresnel functions. The results confirm the close relationship between fractional calculus and Bessel functions, proposing new perspectives for applications in mathematical physics.

 

Author(s) Details :-

 

Jorge Olivares Funes
Department of Mathematics, Universidad de Antofagasta, Antofagasta, Chile.

 

Pablo Martin
Department of Physics, Universidad de Antofagasta, Antofagasta, Chile.

 

Elvis Valero Kari
Universidad Mayor de San Andres, Bolivia.

 

Maria Teresa Veliz Aviles
Department of Physics, Universidad de Antofagasta, Antofagasta, Chile.

 

Please see the book here :- https://doi.org/10.9734/bpi/psniad/v4/6785

Analytical Solution of the Hyperbolic Heat Conduction Equation for Moving Semi-infinite Medium under the Effect of Time dependent Laser Heat Source| Chapter 8 | Research Highlights in Mathematics and Computer Science Vol. 5

 Thermal broadcast issues of moving material radio under the influence of laser heat beginnings have attracted the consideration of many researchers due to their variety of applications.And taking everything in mind the continuous increase of those researches and uses, we have found in this chapter the examining solution to the embellished thermal generated power equation for a semi-limitless moving medium, that was presented by Christov and Jordan [2] in the year 2005 AD.

Author(s) Details:

Reem T. Al-Khairy,
Abdul Rahman Bin Faisal University, Saudi Arabia.

Zakiah M. Al-Ofey,
Abdul Rahman Bin Faisal University, Saudi Arabia.

Please see the link here: https://stm.bookpi.org/RHMCS-V5/article/view/9416

A New Analysis and Derivations of Properties of Ideal and Fractional Capacitors by Application of New Generalized Formula of Charge Function q(t) = c(t)*v(t)| Chapter 6 | New Frontiers in Physical Science Research Vol. 3

 This episode is continuation of application of a recently developed statement formula for capacitor i.e. charge as a function momentary, which is spiral operation of a time variable capacity function and a period-varying voltage function (various from capacitance multiplied by physical ability to get charge stored in a capacitor). This stage gives a theoretical lawfulness test i.e. analytically acquired in several applications for this new expression. This chapter will suffice in various super-capacitor studies, dielectric entertainment experiments, and impedance spectroscopy for miscellaneous material developments for electrical strength storage responsibilities. This new generalized formula is too verified tentatively. Here we use this new expression and apply to differing types of input excitement voltages those are-sinusoidal, constant step, ramp strength We analyze and define the effects, like the charge, the current, the loss-touching and the memory effects, remembering shape of input potential and extend this to evaluate resistance function of a classical capacitor in addition to a fractional capacitor. We also obtain by using this new rule to get value of equivalent Farads for a partial capacitor having parts in fractional order elaborated on the Nyquist’s drawing.  However, this concept is still to be used to its adequate potential.

Author(s) Details:

Shantanu Das,
Bhabha Atomic Research Center (BARC), Mumbai, India.

Please see the link here: https://stm.bookpi.org/NFPSR-V3/article/view/8592

Modified Couple Stress Thermoelastic Diffusive Beam Due to Ramp Type Heating | Chapter 10 | New Visions in Science and Technology Vol. 6

 Due to ramp type heating, this chapter depicts the thermoelastic diffusion beam in modified couple stress theory. To address the problem in non-dimensional form, the Euler-Bernoulli beam theory, Laplace transform technique, and eigenvalue approach are used. The basic equations are written in the form of a vector-matrix differential equation, which is solved using the eigenvalue approach, using Euler-Bernoulli beam theory and the Laplace transform technique. Displacement, lateral deflection, temperature, axial tension, chemical potential, and concentration components are converted. To recover the solutions in the physical domain, a numerical inversion technique was used. With the help of MATLAB software, the analytical results were numerically determined. Mathematical modelling is done with copper substance. For various time values, numerically simulated results for displacement, lateral deflection, temperature, axial stress, chemical potential, and concentration are graphically presented. For various time values, comparisons have been done. In the problem, certain specific instances are discussed.

Author (S) Details

 

Shaloo Devi

Department of Mathematics, Maharaja Lakshman Sen Memorial College, Sundernagar, Mandi, Himachal Pradesh, India.

View Book :- https://stm.bookpi.org/NVST-V6/article/view/4141

The Investigation of the Effects of Banana Maturity on the Drying Kinetics of Thinly-Sliced Saba (Musa balbasiana) Using Hot-Air Dryer | Chapter 10 | New Approaches in Engineering Research Vol. 16

 Banana is one of the most widely grown crops in the Philippines, and one of the most popular varieties is Musa balbasiana, sometimes known as Saba. Saba is perishable due to its high moisture content, and drying is one way to extend its shelf life. It must be consumed within a few days of harvesting due to its short shelf life. Saba's shelf life can be extended by up to six months if dried to a moisture content of 12 percent. The study focuses on the impact of banana ripeness and selects a mathematical model that best fits the drying kinetics of the fruit. The banana samples, both unripe and ripe Saba, were bone-dried in a hot-air tray drier without any pre-treatment. Three experiments were conducted at temperatures of 40°C, 50°C, and 60°C to provide repeatable results. The treated data for both unripe and ripe Saba best suited the Laplace Transform Model out of the three mathematical models utilised in the study. The time per trial was calculated using Lagrange interpolation; for the three trials, unripe Saba dried at 50°C achieved the optimal moisture content in an average time of 87.5574 minutes, while ripe Saba dried at 40°C obtained the same moisture content in an average time of 88.8619 minutes. The discoloration diminished as the temperature rose, demonstrating that browning was enzymatic. When it comes to determining the drying time, the difference in the amount of moisture that can be removed from Saba is a bigger factor than the temperature.

Author(S) Details

Lola Domnina Pestaño
Chemical Engineering Department, Faculty of Engineering, University of Santo Tomas, Philippines. and Research Center for the Natural and Applied Sciences, University of Santo Tomas, Philippines.

John Paul Bautista
Chemical Engineering Department, Faculty of Engineering, University of Santo Tomas, Philippines.

Reizl Leguiab
Chemical Engineering Department, Faculty of Engineering, University of Santo Tomas, Philippines.

Sean Danielle Puri
Chemical Engineering Department, Faculty of Engineering, University of Santo Tomas, Philippines.

View Book:- https://stm.bookpi.org/NAER-V16/article/view/4063

Differential Equations, Special Functions, Laplace Transform by Differential Calculus | Chapter 10 | New Insights into Physical Science Vol.3

A formula changing the operator ) B(g)A(f where I ˆBAAB  into a sum of operators !k/)A(f)B(g )k()k( is proved. Thank to this relation between operators a new and rapid method for resolutions of differential equations is exposed in details. It is seen to be useful also for obtaining the differential operators that transform monomials into Hermite, Laguerre, associated Laguerre, Gegenbauer, Chebyshev polynomials and for getting quasi all their main properties in a very concise manner. Is proposed also the differential representation of the Laplace transform permitting the differential calculus to prove consicely its properties.

Author (s) Details

Do Tan Si
HoChiMinhCity Physical Association, Vietnam, 40 Dong Khoi, Q1, HochiMinhcity, Vietnam and Universite libre de Bruxelles, UEM, Belgium.

View Book :- http://bp.bookpi.org/index.php/bpi/catalog/book/214