In this work, we suggest a new numerical scheme called the fractional higher order Taylor method (FHOTM) to solve fractional differential equations (FDEs). Using the generalized Taylor’s theorem is the fundamental concept of this approach. Then, the local truncation error generated by the suggested FHOTM is estimated by proving suitable theoretical results. At last, several numerical applications are given to demonstrate the applicability of the suggested approach in relation to their exact solutions.

Iqbal M. Batiha

Iqbal H. Jebril

Amira Abdelnebi

Zoubir Dahmani

Shawkat Alkhazaleh

Nidal Anakira

A New Fractional Representation of the Higher Order Taylor Scheme

This article proposes a collocation approach based on a redefined quintic B-spline basis for solving the time-fractional Whitham-Broer-Kaup equations. The presented method involves discretizing the time-fractional derivatives using an <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.1815pt" id="M1" height="11.8174pt" version="1.1" viewBox="-0.0498162 -8.6359 13.3712 11.8174" width="13.3712pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-77" d="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"/></g><g transform="matrix(.0091,0,0,-0.0091,8.294,3.132)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g></svg>-</span>approximation scheme and then approximating the spatial derivatives using the redefined quintic B-spline basis. The von Neumann technique has been used to demonstrate that the proposed method is unconditionally stable. The error estimates are discussed and show that the proposed method is third-order convergent. The results demonstrate the potential of the proposed method as a reliable tool for solving fractional differential equations.

Adel R. Hadhoud

Abdulqawi A. M. Rageh

Redefined Quintic B-Spline Collocation Method to Solve the Time-Fractional Whitham-Broer-Kaup Equations

In this study, we present a mathematical model for the codynamics of taeniasis and neurocysticercosis and rigorously analyze it. To understand the underlying dynamics of the proposed model, basic system properties such as the positivity and boundedness of solutions are investigated through the completing differential process. The basic reproduction number was calculated using the next-generation matrix method, and the analysis showed that when <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="28.481pt" style="vertical-align:-3.29108pt" id="M1" height="12.3054pt" version="1.1" viewBox="-0.0498162 -9.01432 28.481 12.3054"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g198-19" d="M852 669C820 657 792 643 768 628C705 667 627 687 547 687C310 687 154 548 154 412C154 332 212 282 296 282C434 282 515 426 523 557H503C474 402 410 312 298 312C241 312 195 352 195 408C195 535 341 657 546 657C613 657 683 644 738 609C640 538 574 431 486 271C374 71 314 16 189 16C118 16 69 60 69 95H71C78 84 93 83 101 83C129 83 144 106 144 131C144 160 121 179 93 179C60 179 34 151 34 108C34 42 100 -15 207 -15C364 -15 491 73 603 304C614 297 639 293 650 293C681 293 683 254 683 245C683 181 599 150 599 70C599 21 645 -12 692 -12C747 -12 804 30 868 103L851 119C789 52 741 18 706 18C685 18 674 29 674 52C674 92 750 157 750 226C750 257 727 287 696 310V312C812 315 876 394 876 473C876 525 849 577 793 612C812 627 832 639 859 650L852 669ZM814 486C814 417 765 345 686 337C669 348 649 354 626 354C673 451 708 533 766 588C799 561 814 525 814 486Z"/></g><g transform="matrix(.0091,0,0,-0.0091,12.272,3.132)"><path id="g50-49" d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"/></g><g transform="matrix(.013,0,0,-0.013,20.85,0)"><path id="g117-91" d="M512 -3V55L134 254V256L512 456V514L75 281V230L512 -3Z"/></g></svg><span class="irelop"></span><span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="6.438pt" style="vertical-align:-3.29108pt" height="12.3054pt" version="1.1" viewBox="32.0631838 -9.01432 6.438 12.3054"><g transform="matrix(.013,0,0,-0.013,32.113,0)"><path id="g113-50" d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"/></g></svg>,</span></span> the disease in the community eventually dies out, and when <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="28.481pt" style="vertical-align:-3.29108pt" id="M2" height="12.3054pt" version="1.1" viewBox="-0.0498162 -9.01432 28.481 12.3054"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g198-19"/></g><g transform="matrix(.0091,0,0,-0.0091,12.272,3.132)"><use xlink:href="#g50-49"/></g><g transform="matrix(.013,0,0,-0.013,20.85,0)"><path id="g117-92" d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z"/></g></svg><span class="irelop"></span><span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="6.438pt" style="vertical-align:-3.29108pt" height="12.3054pt" version="1.1" viewBox="32.0631838 -9.01432 6.438 12.3054"><g transform="matrix(.013,0,0,-0.013,32.113,0)"><use xlink:href="#g113-50"/></g></svg>,</span></span> the diseases persist. Local stability of the equilibria was analyzed using the Jacobian matrix, and Lyapunov function techniques were used to determine the global analysis, which showed that the endemic equilibrium point was globally stable when <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="28.481pt" style="vertical-align:-3.29108pt" id="M3" height="12.3054pt" version="1.1" viewBox="-0.0498162 -9.01432 28.481 12.3054"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g198-19"/></g><g transform="matrix(.0091,0,0,-0.0091,12.272,3.132)"><use xlink:href="#g50-49"/></g><g transform="matrix(.013,0,0,-0.013,20.85,0)"><use xlink:href="#g117-92"/></g></svg><span class="irelop"></span><span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="6.438pt" style="vertical-align:-3.29108pt" height="12.3054pt" version="1.1" viewBox="32.0631838 -9.01432 6.438 12.3054"><g transform="matrix(.013,0,0,-0.013,32.113,0)"><use xlink:href="#g113-50"/></g></svg>.</span></span> On the other hand, the disease-free equilibrium was determined to be globally stable when <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="28.481pt" style="vertical-align:-3.29108pt" id="M4" height="12.3054pt" version="1.1" viewBox="-0.0498162 -9.01432 28.481 12.3054"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g198-19"/></g><g transform="matrix(.0091,0,0,-0.0091,12.272,3.132)"><use xlink:href="#g50-49"/></g><g transform="matrix(.013,0,0,-0.013,20.85,0)"><use xlink:href="#g117-91"/></g></svg><span class="irelop"></span><span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="6.438pt" style="vertical-align:-3.29108pt" height="12.3054pt" version="1.1" viewBox="32.0631838 -9.01432 6.438 12.3054"><g transform="matrix(.013,0,0,-0.013,32.113,0)"><use xlink:href="#g113-50"/></g></svg>.</span></span> To identify the most influential parameters of the proposed model, partial correlation coefficient techniques were used. The numerical results depict that the model aligns well with the transmission dynamics, which goes through two populations: humans and pigs, whereby the model system stabilizes after some time, showing the validity of the proposed model. Furthermore, the simulations of the proposed model revealed that the shedding habit of infected humans with taeniasis and the bad cooking habit or eating of raw or undercooked pork products have a higher impact on the spread of neurocysticercosis and taeniasis in the community. Hence, this study proposes that in order to control taeniasis and neurocysticercosis, effective disease control measures should primarily prioritize hygienic behaviour and proper cooking of pork meat to the required temperature.

Gideon Eustace Rwabona

Verdiana Grace Masanja

Sayoki Mfinanga

Abdoelnaser Degoot

Silas Mirau

A Mathematical Model for Transmission of Taeniasis and Neurocysticercosis

In this study, Secant Kumaraswamy family of distributions is proposed and studied. This is motivated by the fact that no one distribution can model all types of data from different fields. Therefore, there is the need to develop distributions with desirable properties and flexible enough for modelling data exhibiting different characteristics. Some properties of the new family of distributions, including the quantile function, moments, moment generating function, and mean residual life function, are derived. Five special cases of the family of distributions are presented, and their flexibility is shown by the varying degrees of skewness and kurtosis and nonmonotonic hazard rates. The maximum likelihood estimation method is used to obtain estimators of the family of distributions. Two location-scale regression models are developed for the Secant Kumaraswamy Weibull distribution, which is a special case of the family of distributions. Six different real datasets are used to demonstrate the usefulness of the family of distributions and the regression models. The results show that the family of distributions can be used to model real datasets.

Salifu Nanga

Shei Baba Sayibu

Irene Dekomwine Angbing

Mubarika Alhassan

Abdul-Majeed Benson

Abdul Ghaniyyu Abubakari

Suleman Nasiru

Secant Kumaraswamy Family of Distributions: Properties, Regression Model, and Applications

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<p><em>Computational and Mathematical Methods</em>&nbsp;is an interdisciplinary journal dedicated to publishing the world's top research in the expanding area of computational mathematics, science and engineering.&nbsp;</p>


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<p>Chief Editor, Professor Jesús Vigo Aguiar, is based at University of Salamanca, Spain.&nbsp;His core expertise is in mathematical applications.&nbsp;</p>


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Computational and Mathematical Methods is an interdisciplinary journal dedicated to publishing the world's top research in the expanding area of computational mathematics, science and engineering. 

Computational and Mathematical Methods