Browsing by Author "Jarunee Soontharanon"

Now showing 1 - 16 of 16
  • Default Image
    Item
    A coupled system of fractional difference equations with nonlocal fractional sum boundary conditions on the discrete half-line
    (MDPI AG, 2019) Jarunee Soontharanon; Saowaluck Chasreechai; Thanin Sitthiwirattham; S. Chasreechai; Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand; email: saowaluck.c@sci.kmutnb.ac.th
    In this article, we propose a coupled system of fractional difference equations with nonlocal fractional sum boundary conditions on the discrete half-line and study its existence result by using Schauder's fixed point theorem. An example is provided to illustrate the results. � 2019 by the authors.
  • Default Image
    Item
    Existence results of nonlocal Robin boundary value problems for fractional (p, q) -integrodifference equations
    (Springer, 2020) Jarunee Soontharanon; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, Thailand; email: thanin_sit@dusit.ac.th
    The existence results of a fractional (p, q) -integrodifference equation with nonlocal Robin boundary condition are investigated by using BanachÕs and SchauderÕs fixed point theorems. Moreover, we study some properties of (p, q) -integral that will be used as a tool for our calculations. © 2020, The Author(s).
  • Default Image
    Item
    FRACTIONAL HERMITE-HADAMARD INEQUALITY AND ERROR ESTIMATES FOR SIMPSONÕS FORMULA THROUGH CONVEXITY WITH RESPECT TO A PAIR OF FUNCTIONS
    (University of Miskolc, 2023) Muhammad Aamir Ali; Jarunee Soontharanon; HŸseyin Budak; Thanin Sitthiwirattham; Michal Fe_kan; M. Fe_kan; Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Bratislava, Mlynsk‡ dolina, 842 48, Slovakia; email: michal.feckan@fmph.uniba.sk
    In this article, we establish two new and different versions of fractional Hermite-Hadamard type inequality for the convex functions with respect to a pair of functions. Moreover, we establish a new SimpsonÕs type inequalities for differentiable convex functions with respect to a pair of functions. We also prove two more SimpsonÕs type inequalities for differentiable convex functions with respect to a pair of functions using the power mean and HšlderÕs inequalities. It is also shown that the newly established inequalities are the extension of some existing results. Finally, we add some mathematical examples and their graphs to show the validity of newly established results. © 2023 Miskolc University Press
  • Default Image
    Item
    New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions
    (University of Maragheh, 2025) Jarunee Soontharanon; Muhammad Aamir Ali; Shahram Rezapour; Muhammad Toseef; Thanin Sitthiwirattham; S. Rezapour; Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran; email: rezapourshahram@yahoo.ca
    The main objective of this paper is to establish some new inequalities related to the open Newton-Cotes formulas in the setting of q-calculus. We establish a quantum integral identity first and then prove the desired inequalities for q-differentiable convex functions. These inequalities are useful for determining error bounds for the open Newton-Cotes formulas in both classical and q-calculus. This work distinguishes itself from existing studies by employing quantum operators, leading to sharper and more precise error estimates. These results extend the applicability of Newton-Cotes methods to quantum calculus, offering a novel contribution to the numerical analysis of convex functions. Finally, we provide mathematical examples and computational analysis to validate the newly established inequalities. © 2025 University of Maragheh. All rights reserved.
  • Default Image
    Item
    On fractional (p, q) -calculus
    (Springer, 2020) Jarunee Soontharanon; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, Thailand; email: thanin_sit@dusit.ac.th
    In this paper, the new concepts of (p, q) -difference operators are introduced. The properties of fractional (p, q) -calculus in the sense of a (p, q) -difference operator are introduced and developed. © 2020, The Author(s).
  • Default Image
    Item
    On periodic fractional (P, q)-integral boundary value problems for sequential fractional (p, q)-integrodifference equations
    (MDPI, 2021) Jarunee Soontharanon; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    We study the existence results of a fractional (p, q)-integrodifference equation with periodic fractional (p, q)-integral boundary condition by using Banach and SchauderÕs fixed point theorems. Some properties of (p, q)-integral are also presented in this paper as a tool for our calculations. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
  • Default Image
    Item
    On positive solution to multi-point fractional h-sum eigenvalue problems for caputo fractional h-difference equations
    (University of Nis, 2018) Saowaluck Chasreechai; Jarunee Soontharanon; Thanin Sitthiwirattham
    In this article, we study the existence of at least one positive solution to a multi-point fractional h-sum eigenvalue problem for Caputo fractional h-difference equation, by using the Guo-Krasnoselskii�s fixed point theorem. Moreover, we present some examples to display the importance of these results. � 2018, University of Nis. All rights reserved.
  • Default Image
    Item
    On sequential fractional Caputo (p, q)-integrodifference equations via three-point fractional riemann-liouville (p, q)-difference boundary condition
    (American Institute of Mathematical Sciences, 2022) Jarunee Soontharanon; Thanin Sitthiwirattham; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin.sit@dusit.ac.th
    In this paper, we aim to study the problem of a sequential fractional Caputo (p, q)-integrodifference equation with three-point fractional Riemann-Liouville (p, q)-difference boundary condition. We use some properties of (p, q)-integral in this study and employ Banach fixed point theorems and SchauderÕs fixed point theorems to prove existence results of this problem. © 2022 the Author(s), licensee AIMS Press.
  • Default Image
    Item
    On some error bounds of MaclaurinÕs formula for convex functions in q-calculus
    (University of Nis, 2023) Thanin Sitthiwirattham; Muhammad Aamir Ali; Jarunee Soontharanon; M.A. Ali; School of Mathematical Sciences, Nanjing Normal University, China; email: mahr.muhammad.aamir@gmail.com
    The main goal of this paper is to establish some error bounds for MaclaurinÕs formula which is three point quadrature formula using the notions of q-calculus. For this, we first prove a q-integral identity involving fist time q-differentiable functions. Then, by using the new established identity we find the error bounds for maclaurinÕs formula by using the convexity of fist time q-differentiable functions. It is also shown that the newly established inequalities are extension of some existing inequalities inside the literature. © 2023, University of Nis. All rights reserved.
  • Default Image
    Item
    On some new Hermite-Hadamard and Ostrowski type inequalities for s-convex functions in (p, q)-calculus with applications
    (De Gruyter Open Ltd, 2022) Xue-Xiao You; Muhammad Aamir Ali; Humaira Kalsoom; Jarunee Soontharanon; Thanin Sitthiwirattham; M.A. Ali; Jiangsu Key Laboratory for Nslscs, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.com; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    In this study, we establish some new Hermite-Hadamard type inequalities for s-convex functions in the second sense using the post-quantum calculus. Moreover, we prove a new (p, q)\left(p,q)-integral identity to prove some new Ostrowski type inequalities for (p, q)\left(p,q)-differentiable functions. We also show that the newly discovered results are generalizations of comparable results in the literature. Finally, we give application to special means of real numbers using the newly proved inequalities. © 2022 Xue-Xiao You et al., published by De Gruyter.
  • Default Image
    Item
    On some new inequalities of hermiteÐhadamard midpoint and trapezoid type for preinvex functions in (P, q)-calculus
    (MDPI, 2021) Ifra Bashir Sial; Muhammad Aamir Ali; Ghulam Murtaza; Sotiris K. Ntouyas; Jarunee Soontharanon; Thanin Sitthiwirattham; M.A. Ali; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.com; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    In this paper, we establish some new HermiteÐHadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for (p, q)-differentiable preinvex functions in the context of (p, q)-calculus. We also show that the results established in this paper are generalizations of comparable results in the literature of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
  • Default Image
    Item
    On some new trapezoidal type inequalities for twice (P, q) differentiable convex functions in post-quantum calculus
    (MDPI, 2021) Thanin Sitthiwirattham; Ghulam Murtaza; Muhammad Aamir Ali; Sotiris K. Ntouyas; Muhammad Adeel; Jarunee Soontharanon; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and symmetry, has various applications for quantum calculus. Inequalities has a strong association with convex and symmetric convex functions. In this study, first we establish a (p,q)-integral identity involving the second (p,q)-derivative and then we used this result to prove some new trapezoidal type inequalities for twice (p,q)-differentiable convex functions. It is also shown that the newly established results are the refinements of some existing results in the field of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. © 2021 by the authors.
  • Default Image
    Item
    Several integral inequalities of hermiteÐhadamard type related to k-fractional conformable integral operators
    (MDPI, 2021) Muhammad Tariq; Soubhagya Kumar Sahoo; Hijaz Ahmad; Thanin Sitthiwirattham; Jarunee Soontharanon; H. Ahmad; Section of Mathematics, International Telematic University Uninettuno, Roma, Corso Vittorio Emanuele II 39, 00186, Italy; email: f17ppbsi011@uetpeshawar.edu.pk; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    In this paper, we present some ideas and concepts related to the k-fractional conformable integral operator for convex functions. First, we present a new integral identity correlated with the k-fractional conformable operator for the first-order derivative of a given function. Employing this new identity, the authors have proved some generalized inequalities of HermiteÐHadamard type via HšlderÕs inequality and the power mean inequality. Inequalities have a strong correlation with convex and symmetric convex functions. There exist expansive properties and strong correlations between the symmetric function and various areas of convexity, including convex functions, probability theory, and convex geometry on convex sets because of their fascinating properties in the mathematical sciences. The results of this paper show that the methodology can be directly applied and is computationally easy to use and exact. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
  • Default Image
    Item
    Some New Generalized Fractional Newton's Type Inequalities for Convex Functions
    (Hindawi Limited, 2022) Jarunee Soontharanon; Muhammad Aamir Ali; HŸseyin Budak; Pinar Kšsem; Kamsing Nonlaopon; Thanin Sitthiwirattham; K. Nonlaopon; Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand; email: nkamsi@kku.ac.th
    In this paper, we establish some new Newton's type inequalities for differentiable convex functions using the generalized Riemann-Liouville fractional integrals. The main edge of the newly established inequalities is that these can be turned into several new and existing inequalities for different fractional integrals like Riemann-Liouville fractional integrals, k-fractional integrals, Katugampola fractional operators, conformable fractional operators, Hadamard fractional operators, and fractional operators with the exponential kernel without proving one by one. It is also shown that the newly established inequalities are the refinements of the previously established inequalities inside the literature. © 2022 Jarunee Soontharanon et al.
  • Default Image
    Item
    Study of implicit-impulsive differential equations involving Caputo-Fabrizio fractional derivative
    (American Institute of Mathematical Sciences, 2022) Thanin Sitthiwirattham; Rozi Gul; Kamal Shah; Ibrahim Mahariq; Jarunee Soontharanon; Khursheed J. Ansari; K. Shah; Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan; email: kamalshah408@gmail.com
    This article is devoted to investigate a class of non-local initial value problem of implicit-impulsive fractional differential equations (IFDEs) with the participation of the Caputo-Fabrizio fractional derivative (CFFD). By means of KrasnoselskiiÕs fixed-point theorem and BanachÕs contraction principle, the results of existence and uniqueness are obtained. Furthermore, we establish some results of Hyers-Ulam (H-U) and generalized Hyers-Ulam (g-H-U) stability. Finally, an example is provided to demonstrate our results. © 2022 the Author(s),.
  • Default Image
    Item
    Three-point fractional h-sum boundary value problems for sequential caputo fractional h-sum-difference equations
    (University of Nis, 2017) Jarunee Soontharanon; Jiraporn Reunsumrit; Thanin Sitthiwirattham
    In this article, we study an existence and uniqueness results for a sequential nonlinear Caputo fractional h-sum-difference equation with three-point fractional h-sum boundary conditions, by using the Banach contraction principle and the Schauder�s fixed point theorem. Our problem contains different orders in three fractional difference operators and three fractional sums. Finally, we provide an example to displays the importance of these results. � 2017, University of Nis. All rights reserved.