International Scientific Research PublicationsMathematics in Natural Science(MNS)1120171022The non-linear Dodson diffusion equation: Approximate solutions and beyond with formalistic fractionalization117http://dx.doi.org/10.22436/mns.01.01.01ENJ.HristovDepartment 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)1120171022New direction in fractional differentiation1825http://dx.doi.org/10.22436/mns.01.01.02ENA.AtanganaInstitute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300, Bloemfontein, South Africa.I.KocaDepartment 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)11Generalized fractional calculus of the multiindex Bessel function2632http://dx.doi.org/10.22436/mns.01.01.03END. L.SutharS. D.PurohitR. K.Parmarhttp://isr-publications.com/mns/5022/download-generalized-fractional-calculus-of-the-multiindex-bessel-functionInternational Scientific Research PublicationsMathematics in Natural Science(MNS)1120171019A 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-type