International Scientific Research PublicationsMathematics in Natural Science(MNS)ISSN 2600-76651120171022The non-linear Dodson diffusion equation: Approximate solutions and beyond with formalistic fractionalization117http://dx.doi.org/10.22436/mns.01.01.01ENJordanHristovDepartment of Chemical Engineering, University of Chemical Technology and Metallurgy, Sofia 1756, 8 Kliment Ohridsky, blvd. Bulgaria The Dodson mass diffusion equation with exponentially diffusivity is analyzed through approximate integral solutions.
Integral-balance solutions were developed to integer-order versions as well as to formally fractionalized models. The formal
fractionalization considers replacement of the time derivative with a fractional version with either singular (Riemann-Liouville
or Caputo) or non-singular fading memory. The solutions developed allow seeing a new side of the Dodson equation and
to separate the formal fractional model with Caputo-Fabrizio time derivative with an integral-balance allowing relating the
fractional order to the physical relaxation time as adequate to the phenomena behind.
http://isr-publications.com/mns/4994/download-the-non-linear-dodson-diffusion-equation-approximate-solutions-and-beyond-with-formalistic-fractionalizationInternational Scientific Research PublicationsMathematics in Natural Science(MNS)ISSN 2600-76651120171022New direction in fractional differentiation1825http://dx.doi.org/10.22436/mns.01.01.02ENAbdonAtanganaInstitute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300, Bloemfontein, South Africa.IlknurKocaDepartment of Mathematics, Faculty of Sciences, Mehmet Akif Ersoy University, 15100, Burdur, Turkey. Based upon the Mittag-Leffler function, new derivatives with fractional order were constructed. With the same line of
idea, improper derivatives based on the Weyl approach are constructed in this work. To further model some complex physical
problems that cannot be modeled with existing derivatives with fractional order, we propose, a new derivative based on the
more generalized Mittag-Leffler function known as Prabhakar function. Some new results are presented together with some
applications.
http://isr-publications.com/mns/5021/download-new-direction-in-fractional-differentiationInternational Scientific Research PublicationsMathematics in Natural Science(MNS)ISSN 2600-76651120171022Generalized fractional calculus of the multiindex Bessel function2632http://dx.doi.org/10.22436/mns.01.01.03END. L.SutharDepartment of Mathematics, Wollo University, Dessie, Ethiopia.S. D.PurohitDepartment of HEAS (Mathematics), Rajasthan Technical University, Kota 324010, Rajasthan, India.R. K.ParmarDepartment of Mathematics, Government College of Engineering and Technology, Bikaner-334004, India.The present paper is devoted to the study of the fractional calculus operators to obtain a number of key results for the
generalized multiindex Bessel function involving Saigo hypergeometric fractional integral and differential operators in terms
of generalized Wright function. Various particular cases and consequences of our main fractional-calculus results as classical
Riemann-Liouville and Erde´lyi-Kober fractional integral and differential formulas are deduced.
http://isr-publications.com/mns/5022/download-generalized-fractional-calculus-of-the-multiindex-bessel-functionInternational Scientific Research PublicationsMathematics in Natural Science(MNS)ISSN 2600-76651120171025A uniqueness theorem for eigenvalue problem having special potential type3339http://dx.doi.org/10.22436/mns.01.01.04ENErdal BasDepartment of Mathematics, Faculty of Science, Firat University, Elazig, 23119, TurkeyEtibar S. PanakhovDepartment of Mathematics, Faculty of Science, Firat University, Elazig, 23119, TurkeyResat YilmazerDepartment of Mathematics, Faculty of Science, Firat University, Elazig, 23119, Turkey In this study, a uniqueness theorem is given for
Sturm-Liouville problem with special singular potential. We prove that
singular potential function can be uniquely determined by the spectral set \(
\left\{ \lambda _{n}\left( q_{0},h_{m}\right) \right\} _{m=1}^{+\infty }.\)
http://isr-publications.com/mns/5854/download-a-uniqueness-theorem-for-eigenvalue-problem-having-special-potential-typeInternational Scientific Research PublicationsMathematics in Natural Science(MNS)ISSN 2600-76651120171101Stochastic fixed point theorems for a random Z-contraction in a complete probability measure space with application to non-linear stochastic integral equations4048http://dx.doi.org/10.22436/mns.01.01.05ENPlern SaiparaKMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandPoom KumamKMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandApirak SombatKMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandAnantachai PadcharoenKMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandWiyada KumamProgram in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Thanyaburi (RMUTT), Pathumthani 12110, ThailandIn this paper, we propose the random \(\mathcal{Z}\)-contraction, prove a stochastic fixed point theorem for this contraction, and show that a solution for a non-linear stochastic integral equations exists in Banach spaces.
http://isr-publications.com/mns/5982/download-stochastic-fixed-point-theorems-for-a-random-z-contraction-in-a-complete-probability-measure-space-with-application-to-non-linear-stochastic-integral-equations