Fractional q-Difference Equation
Existence of positive solutions for two point boundary value problems of nonlinear fractional q difference equation
... about fractional q-calculus and fractional q-differential equation ...the fractional quantum difference equation has also attracted the attention of many researchers in ...
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Monotone iterative technique for a nonlinear fractional q difference equation of Caputo type
... By establishing a comparison theorem and applying the monotone iterative technique combined with the method of lower and upper solutions, we investigate the existence of extremal solutions of the initial value problem ...
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Existence of Positive Solutions for Boundary Value Problem of Nonlinear Fractional q Difference Equation
... Al-Askar, “On the Existence of Positive Solutions for a Boundary Value Problem of Fracntional Order,” International Journal of Mathematical Analysis, Vol.. Lü, “Positive Solutions for Bo[r] ...
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Existence of solutions for fractional q difference equation with mixed nonlinear boundary conditions
... As is well known, the aim of finding solutions to boundary value problems is of main importance in various fields of applied mathematics. Recently, there seems to be a new interest in the study of the boundary value ...
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Positive and negative solutions of a boundary value problem for a fractional q difference equation
... for q-derivatives. So boundary value problems for fractional q-difference equations have become of importance and the existence of positive solutions has been studied by a great number of researchers; ...
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Existence of positive solutions of nonlinear fractional q difference equation with parameter
... The q-difference calculus is an interesting and old subject that many researchers devote their time to ...The q-difference calculus or quantum calculus were first developed by Jackson [, ], while basic ...
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A Cauchy Problem for Some Fractional q Difference Equations with Nonlocal Conditions
... In this paper, we discussed the problem of nonlocal value for nonlinear fractional q-difference equation. The classical tools of fixed point theorems such as Krasnoselskii’s theorem and ...
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Existence of solutions for fractional q integro difference inclusions with fractional q integral boundary conditions
... Fractional q-difference equations, known as fractional analogue of q-difference equa- tions, have recently been discussed by several ...type q-difference (integral) equation with ...
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Ulam stability of Caputo q fractional delay difference equation: q fractional Gronwall inequality approach
... discrete fractional Gronwall inequality for the first time ...and fractional dynami- cal ...a fractional differential ...the fractional Gronwall in- equality and used it in the qualitative ...
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On nonlocal fractional q-integral boundary value problems of fractional q-difference and fractional q-integrodifference equations involving different numbers of order and q
... on q-integral boundary value problems, we refer to [–] and the references cited ...nonlinear fractional q-difference equation with nonlocal and sub-strip type boundary ...
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Existence and Ulam stability for implicit fractional q difference equations
... Fractional q-difference equations were initiated in the beginning of the 19th century [7, 15], and received significant attention in recent ...of q-difference and fractional q-difference ...
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Boundary value problems for fractional q difference equations with nonlocal conditions
... a fractional q-difference equation with nonlocal conditions involving the fractional q-derivative of the Caputo type, and the nonlinear term contains a fractional ...
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Existence results for fractional q difference equations with nonlocal q integral boundary conditions
... nonlinear q-difference equations is still in the initial stage and many aspects of this theory need to be ...of fractional q-difference equations, for example, [, –, ] and the references ...
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Stability and asymptotic properties of a linear fractional difference equation
... Our last remark concerns an algebraic decay of the solutions y(n) of (.) with | – λ | > . By Corollary ., its order is equal to + α. It might be interesting to note that this decay rate is exactly the same as ...
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Existence Results for Nonlinear Fractional Difference Equation
... operator. To the best of our knowledge, this is a pioneering work on discussing initial value problems IVP for short in discrete fractional calculus. Anastassiou 4 defined a Caputo like discrete fractional ...
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New concepts of fractional quantum calculus and applications to impulsive fractional q difference equations
... of q-integration is reduced to a finite sum, which is the restriction of definition of ...of fractional q-integrals and q-derivatives by shifting the point of the origin from zero to be a ...
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New Modified Method of the Chebyshev Collocation Method for Solving Fractional Diffusion Equation
... The fractional partial differential equations (FPDEs) arise in numerous problems of engineering, physics, mathematics, chemistry, biology,and viscoelasticity ( [1], [2], [3], ...[4]).Most fractional ...
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Fractional q difference hybrid equations and inclusions with Dirichlet boundary conditions
... Fractional calculus has evolved into an interesting and popular field of research due to its theoretical development and extensive applications in the mathematical modeling of many real world phenomena occurring in ...
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Iterative Technology in a Singular Fractional Boundary Value Problem with q Difference
... The q-difference calculus or quantum calculus is an old subject and is rich in history and in ...with q-difference (see [1]-[4] and the references ...
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Coupled implicit Caputo fractional q difference systems
... 39. Rassias, Th.M.: On the stability of linear mappings in Banach spaces. Proc. Am. Math. Soc. 72, 297–300 (1978) 40. Rus, I.A.: Ulam stability of ordinary differential equations. Stud. Univ. Babe¸s–Bolyai, Math. LIV(4), ...
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