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Journal of Difference Equations and Applications Volume 21, 2015 - Issue 4
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Articles

Convexity for nabla and delta fractional differences

Jia BaoguoSchool of Mathematics and Computer Science, Zhongshan University, Guangzhou510275, P.R. China;Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE68588-0130, USAView further author information
,
Lynn ErbeDepartment of Mathematics, University of Nebraska-Lincoln, Lincoln, NE68588-0130, USAView further author information
&
Allan PetersonDepartment of Mathematics, University of Nebraska-Lincoln, Lincoln, NE68588-0130, USACorrespondence[email protected]
View further author information
Pages 360-373 | Received 30 Dec 2014, Accepted 18 Jan 2015, Published online: 24 Feb 2015

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Rajendra Dahal, Christopher S. Goodrich & Benjamin Lyons. (2021) Monotonicity results for sequential fractional differences of mixed orders with negative lower bound. Journal of Difference Equations and Applications 27:11, pages 1574-1593.
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Christopher S. Goodrich & Jagan M. Jonnalagadda. (2021) An analysis of polynomial sequences and their application to discrete fractional operators. Journal of Difference Equations and Applications 27:7, pages 1081-1102.
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Christopher S. Goodrich, Benjamin Lyons, Andrea Scapellato & Mihaela T. Velcsov. (2021) Analytical and numerical convexity results for discrete fractional sequential differences with negative lower bound. Journal of Difference Equations and Applications 27:3, pages 317-341.
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Rajendra Dahal & Christopher S. Goodrich. (2019) Mixed order monotonicity results for sequential fractional nabla differences. Journal of Difference Equations and Applications 25:6, pages 837-854.
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Christopher S. Goodrich. (2019) Sharp monotonicity results for fractional nabla sequential differences. Journal of Difference Equations and Applications 25:6, pages 801-814.
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Johnny Henderson. (2019) Existence of local solutions for fractional difference equations with Dirichlet boundary conditions. Journal of Difference Equations and Applications 25:6, pages 751-756.
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Christopher S. Goodrich. (2017) A sharp convexity result for sequential fractional delta differences. Journal of Difference Equations and Applications 23:12, pages 1986-2003.
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Rajendra Dahal & Christopher S. Goodrich. (2017) An almost sharp monotonicity result for discrete sequential fractional delta differences. Journal of Difference Equations and Applications 23:7, pages 1190-1203.
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Feifei Du, Baoguo Jia, Lynn Erbe & Allan Peterson. (2016) Monotonicity and convexity for nabla fractional (q, h)-differences. Journal of Difference Equations and Applications 22:9, pages 1224-1243.
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Pshtiwan Othman Mohammed, Christopher S. Goodrich, Hari Mohan Srivastava, Eman Al-Sarairah & Y. S. Hamed. (2023) A Study of Monotonicity Analysis for the Delta and Nabla Discrete Fractional Operators of the Liouville–Caputo Family. Axioms 12:2, pages 114.
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Pshtiwan Othman Mohammed & Musawa Yahya Almusawa. (2023) On analysing discrete sequential operators of fractional order and their monotonicity results. AIMS Mathematics 8:6, pages 12872-12888.
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Rajendra Dahal & Christopher S. Goodrich. (2021) Analysis of convexity results for discrete fractional nabla operators. Rocky Mountain Journal of Mathematics 51:6.
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Christopher S. Goodrich & Jagan M. Jonnalagadda. (2021) Monotonicity results for CFC nabla fractional differences with negative lower bound. Analysis 41:4, pages 221-229.
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Rajendra Dahal & Christopher S. Goodrich. (2021) Theoretical and numerical analysis of monotonicity results for fractional difference operators. Applied Mathematics Letters 117, pages 107104.
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Christopher S. Goodrich, Jagan M. Jonnalagadda & Benjamin Lyons. (2021) Convexity, monotonicity, and positivity results for sequential fractional nabla difference operators with discrete exponential kernels. Mathematical Methods in the Applied Sciences 44:8, pages 7099-7120.
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Jennifer Bravo, Carlos Lizama & Silvia Rueda. (2021) Second and third order forward difference operator: what is in between?. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 115:2.
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Johnny Henderson & Jeffrey T. Neugebauer. (2021) Existence of Local Solutions for Fractional Difference Equations with Left Focal Boundary Conditions. Fractional Calculus and Applied Analysis 24:1, pages 324-331.
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Jiraporn Reunsumrit & Thanin Sitthiwirattham. (2020) Existence results of fractional delta–nabla difference equations via mixed boundary conditions. Advances in Difference Equations 2020:1.
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Pimchana Siricharuanun, Saowaluck Chasreechai & Thanin Sitthiwirattham. (2020) On a coupled system of fractional sum-difference equations with p-Laplacian operator. Advances in Difference Equations 2020:1.
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Rujira Ouncharoen, Saowaluck Chasreechai & Thanin Sitthiwirattham. (2020) On Nonlinear Fractional Difference Equation with Delay and Impulses. Symmetry 12:6, pages 980.
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Rujira Ouncharoen, Saowaluck Chasreechai & Thanin Sitthiwirattham. (2020) Existence and Stability Analysis for Fractional Impulsive Caputo Difference-Sum Equations with Periodic Boundary Condition. Mathematics 8:5, pages 843.
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Christopher S. Goodrich & Benjamin Lyons. (2020) Positivity and monotonicity results for triple sequential fractional differences via convolution. Analysis 40:2, pages 89-103.
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Neelam Singha & Chandal Nahak. (2020) α-fractionally convex functions. Fractional Calculus and Applied Analysis 23:2, pages 534-552.
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Jiraporn Reunsumrit & Thanin Sitthiwirattham. (2020) On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations. Mathematics 8:4, pages 476.
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Christopher Goodrich & Carlos Lizama. (2020) A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity. Israel Journal of Mathematics 236:2, pages 533-589.
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Rajendra Dahal & Christopher S. Goodrich. (2019) A uniformly sharp convexity result for discrete fractional sequential differences. Rocky Mountain Journal of Mathematics 49:8.
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Christopher S. Goodrich & Matthew Muellner. (2019) An analysis of the sharpness of monotonicity results via homotopy for sequential fractional operators. Applied Mathematics Letters 98, pages 446-452.
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Jarunee Soontharanon, Saowaluck Chasreechai & Thanin Sitthiwirattham. (2019) A Coupled System of Fractional Difference Equations with Nonlocal Fractional Sum Boundary Conditions on the Discrete Half-Line. Mathematics 7:3, pages 256.
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Baoguo Jia, Lynn Erbe & Allan Peterson. (2019) Asymptotic behavior of solutions of fractional nabla q -difference equations . Georgian Mathematical Journal 26:1, pages 21-28.
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Churong Chen, Baoguo Jia, Xiang Liu & Lynn Erbe. (2018) Existence and Uniqueness Theorem of the Solution to a Class of Nonlinear Nabla Fractional Difference System with a Time Delay. Mediterranean Journal of Mathematics 15:6.
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Okkes Ozturk & Resat Yilmazer. (2018) Solutions of the radial Schrödinger equation in hypergeometric and discrete fractional forms. Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 68:1, pages 833-839.
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Christopher S. Goodrich. (2017) Monotonicity and non-monotonicity results for sequential fractional delta differences of mixed order. Positivity 22:2, pages 551-573.
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Christopher S. Goodrich. (2017) A uniformly sharp monotonicity result for discrete fractional sequential differences. Archiv der Mathematik 110:2, pages 145-154.
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Saowaluck Chasreechai & Thanin Sitthiwirattham. (2018) Existence Results of Initial Value Problems for Hybrid Fractional Sum-Difference Equations. Discrete Dynamics in Nature and Society 2018, pages 1-12.
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Guo-Cheng Wu, Dumitru Baleanu & Wei-Hua Luo. (2017) Lyapunov functions for Riemann–Liouville-like fractional difference equations. Applied Mathematics and Computation 314, pages 228-236.
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Lynn Erbe, Christopher S. Goodrich, Baoguo Jia & Allan Peterson. (2017) Monotonicity results for delta fractional differences revisited. Mathematica Slovaca 67:4, pages 895-906.
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Rajendra Dahal, Stanley Drvol & Christopher S. Goodrich. (2017) New monotonicity conditions in discrete fractional calculus with applications to extremality conditions. Analysis 37:3, pages 145-156.
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Lynn Erbe, Christopher S Goodrich, Baoguo Jia & Allan Peterson. (2016) Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions. Advances in Difference Equations 2016:1.
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Jia Baoguo. (2016) The asymptotic behavior of Caputo delta fractional equations. Mathematical Methods in the Applied Sciences 39:18, pages 5355-5364.
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