Fractional Difference Equations with Real Variable
Jinfa Cheng,Yu-Ming Chu +1 more
TL;DR: In this paper, a new kind of the definition of fractional difference, fractional sum, and fractional differential equation is proposed, and some examples to demonstrate several methods of how to solve certain fractional different equations.
read more
Abstract: We independently propose a new kind of the definition of fractional difference, fractional sum, and fractional difference equation, give some basic properties of fractional difference and fractional sum, and give some examples to demonstrate several methods of how to solve certain fractional difference equations.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Some new inequalities of Hermite-Hadamard type for s-convex functions with applications
TL;DR: In this paper, the authors presented several new and generalized Hermite-Hadamard type inequalities for s-convex functions via classical and Riemann-Liouville fractional integrals.
143
Inequalities for α-fractional differentiable functions
TL;DR: An identity and several Hermite-Hadamard type inequalities for conformable fractional integrals are presented and the error estimations for the trapezoidal formula are given.
On Pólya–Szegö and Čebyšev type inequalities via generalized k-fractional integrals
TL;DR: In this article, the generalized k-fractional integral (GKF) was introduced to implement the evaluation of many mathematical problems related to real world applications, and some new important inequalities of Polya-Szego and Cebysev types by use of GKF were presented.
Generalized Gronwall fractional summation inequalities and their applications
Run Xu,Ying Zhang +1 more
TL;DR: In this article, some generalized discrete fractional Gronwall inequalities are developed, which can be used in the qualitative analysis of the solutions to fractional difference equations and summation equations.
On new fractional integral inequalities for p-convexity within interval-valued functions
TL;DR: In this article, a class of convex interval-valued functions via the Katugampola fractional integral operator is investigated, and integral inequalities of the Hermite-Hadamard type and Hermite Hadamard-Fejer type are established.
References
•Book
Theory and Applications of Fractional Differential Equations
Anatoly A. Kilbas,Hari M. Srivastava,Juan J. Trujillo +2 more
- 02 Mar 2006
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
•Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
- 19 May 1993
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Analysis of Fractional Differential Equations
Kai Diethelm,Neville J. Ford +1 more
TL;DR: In this paper, the authors discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order, and investigate the dependence of the solution on the order of the differential equation and on the initial condition.
3.6K
Advances in dynamic equations on time scales
Martin Bohner,Allan Peterson +1 more
- 01 Jan 2003
TL;DR: Agarwal et al. as discussed by the authors proposed a topological approach for solving two-point boundary value problems on infinite-intervals, using the time scales of the time-scales calculus.
Related Papers (5)
Ferhan M. Atıcı,Paul W. Eloe +1 more
- 10 Sep 2008
Igor Podlubny
- 01 Jan 1999
G. V. S. R. Deekshitulu,J. Jagan Mohan +1 more
- 16 Mar 2012