http://www.scitecresearch.com/journals/index.php/jprm/issue/feedJournal of Progressive Research in Mathematics2024-07-04T08:53:38+00:00Managing Editorjprmeditor@scitecresearch.comOpen Journal SystemsJournal of Progressive Research in Mathematicshttp://www.scitecresearch.com/journals/index.php/jprm/article/view/2225Convexity and Monotonicity Analyses for Discrete Fractional Operators with Discrete Exponential Kernes2024-06-17T06:13:49+00:00Sherif Amirovserifamirov59@gmail.comIhsan Hasan Saadullahihsan.h.sitey@gmail.com<p>For discrete fractional operators with exponential kernels, positivity, monotonicity, and convexity findings are taken into consideration in this paper. Our findings cover both sequential and non-sequential scenarios and show how fractional differences with other kinds of kernels and the exponential kernel example are comparable and different. This demonstrates that the qualitative information gathered in the exponential kernel case does not match other situations perfectly.</p>2024-06-17T06:10:52+00:00##submission.copyrightStatement##http://www.scitecresearch.com/journals/index.php/jprm/article/view/2226Monotonicity Results For Discrete Caputo-Fabrizio Fractional Operators2024-07-04T08:53:38+00:00Sherif Amirovserifamirov59@gmail.comWaad Shaban Mahw Alzebariwaadshaban24@gmail.com<p>Nearly every theory in mathematics has a discrete equivalent that simplifies it theoretically and practically so that it may be used in modeling real-world issues. With discrete calculus, for instance, it is possible to find the "difference" of any function from the first order up to the n-th order. On the other hand, it is also feasible to expand this theory using discrete fractional calculus and make n any real number such that the 1⁄2-order difference is properly defined. This article is divided into five chapters, each of which develops the most straightforward discrete fractional variational theory while illustrating some fundamental concepts and features of discrete fractional calculus. It is also investigated how the idea may be applied to the development of tumors. The first section provides a succinct introduction to the discrete fractional calculus and several key mathematical concepts that are utilized often in the subject. We demonstrate in section 2 that if the Caputo-Fabrizio nabla fractional difference operator of order and commencing at is positive for then is -increasing. On the other hand, if is rising and , then . Additionally, a result of monotonicity for the Caputo-type fractional difference operator is established. We show a fractional difference version of the mean-value theorem as an application and contrast it to the traditional discrete fractional instance.</p>2024-07-04T07:10:16+00:00##submission.copyrightStatement##