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Existence Results for Nonlinear Fractional Difference Equation [PDF]

Advances in Difference Equations, 2011
This paper is concerned with the initial value problem to a nonlinear fractional difference equation with the Caputo like difference operator. By means of some fixed point theorems, global and local existence results of solutions are obtained.
Luo Xiannan, Zhou Yong, Chen Fulai
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Fractional Difference Equations with Real Variable [PDF]

Abstract and Applied Analysis, 2012
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 ...
Jin-Fa Cheng, Yu-Ming Chu
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Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation

International Journal of Applied Mathematics and Computer Science, 2023
This paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov.
Malinowska Agnieszka B., Odzijewicz Tatiana, Poskrobko Anna   +2 more
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Quaternion Fractional Difference with Quaternionic Fractional Order and Applications to Fractional Difference Equation

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
In this paper, we introduce the basic notions of the fractional summation, difference and q-difference with the quaternionic fractional order for the quaternion-valued functions and establish some of their basic properties.
Wang Chao, Xie Weiyu, Agarwal Ravi P.
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Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation [PDF]

The Scientific World Journal, 2013
We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form xn+1=xn-12/(axn2+bxnxn-1+cxn-12),n=0,1,2,…, where the parameters   a,  b, and  c   are positive numbers and the initial ...
M. Garić-Demirović, M. R. S. Kulenović, M. Nurkanović   +2 more
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Nonoscillatory solutions of discrete fractional order equations with positive and negative terms [PDF]

Mathematica Bohemica, 2023
This paper aims at discussing asymptotic behaviour of nonoscillatory solutions of the forced fractional difference equations of the form \align\Delta^{\gamma}u(\kappa)&+\Theta[\kappa+\gamma,w(\kappa+\gamma)] =&\Phi(\kappa+\gamma)+\Upsilon(\kappa ...
Jehad Alzabut, Said Rezk Grace, A. George Maria Selvam, Rajendran Janagaraj   +3 more
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Fractional Order Difference Equations [PDF]

International Journal of Differential Equations, 2012
A difference equation is a relation between the differences of a function at one or more general values of the independent variable. These equations usually describe the evolution of certain phenomena over the course of time. The present paper deals with the existence and uniqueness of solutions of fractional difference equations.
Mohan, J. Jagan, Deekshitulu, G. V. S. R.   +1 more
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Controlling fractional difference equations using feedback

Chaos, Solitons & Fractals, 2023
One of the most popular methods of controlling dynamical systems is feedback. It can be used without acquiring detailed knowledge of the underlying system. In this work, we study the stability of fractional-order linear difference equations under feedback. The stability results are derived for an arbitrary feedback time $τ$. We study the cases of $τ=1$
Divya D. Joshi, Sachin Bhalekar, Prashant M. Gade   +2 more
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Numerical Solution for Riesz Fractional Diffusion Equation via Fractional Centered Difference Scheme

Walailak Journal of Science and Technology, 2021
In this paper, a mixed matrix transform method with fractional centered difference scheme for solving fractional diffusion equation with Riesz fractional derivative was examined.
Sohrab VALIZADEH, Abdollah BORHANIFAR
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Unique iterative solution for nonlinear fractional [BF](p,q)[KG-*2]-[BFQ][KG-*4]difference equation based on [BF]ψ-(h,r)[KG-*2]-[BFQ][KG-*4]concave operators

Journal of Hebei University of Science and Technology, 2022
In order to enrich the basic theory of boundary value problems of fractional (p,q)[KG-*2]-[KG-*3]difference equations,the solvability of nonlocal problems for a class of nonlinear fractional (p,q)[KG-*2]-[KG-*3]difference equations was investigated ...
Jufang WANG, Si WANG, Changlong YU
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