Existence and Uniqueness Theorem of the Solution to a Class of Nonlinear Nabla Fractional Difference System with a Time Delay
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DOI: 10.1007/s00009-018-1258-x
Abstract: In this paper, we investigate an existence and uniqueness theorem of the solution to a class of nonlinear nabla fractional difference system with a time delay. More precisely, observing $$\nu (t-k)^{\overline{\nu -1}}\le {t^{\bar{\nu }}}$$ν(t-k)ν-1¯≤tν¯, we… read more here.
Keywords: fractional difference; difference system; nabla fractional; nonlinear nabla ... See more keywords
Existence of solutions of boundary value problems for singular fractional q-difference equations
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DOI: 10.1007/s12190-016-0994-y
Abstract: In this paper, we study the existence and uniqueness of solutions for a class of singular three-point boundary value problems of fractional q-difference equations invovling fractional q-derivative of Riemann–Liouville type. Based on the generalization of… read more here.
Keywords: difference equations; existence; fractional difference; boundary value ... See more keywords
Fractional difference double sequences of fuzzy numbers
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DOI: 10.1007/s13370-021-00912-7
Abstract: We present double sequence spaces of fuzzy numbers defined using fractional difference operator and Musielak–Orlicz function. Some topological properties for these spaces are presented and some inclusion relations are established. Finally, we formulate and prove… read more here.
Keywords: sequences fuzzy; fuzzy numbers; double sequences; fractional difference ... See more keywords
Unique Solutions for Fractional q-Difference Boundary Value Problems Via a Fixed Point Method
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DOI: 10.1007/s40840-017-0560-2
Abstract: In this paper, by applying the cone theory in ordered Banach spaces associated with the characters of increasing $$\varphi -(h,e)$$φ-(h,e)-concave operators, we investigate the existence and uniqueness of nontrivial solutions for a nonlinear fractional q-difference… read more here.
Keywords: unique solutions; boundary value; solutions fractional; fractional difference ... See more keywords
Existence of local solutions for fractional difference equations with Dirichlet boundary conditions
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Difference Equations and Applications"
DOI: 10.1080/10236198.2018.1505882
Abstract: ABSTRACT For a real number and a natural number, conditions are given for the existence of solutions of the νth-order Atıcı–Eloe fractional difference equation, and satisfying the Dirichlet boundary conditions . read more here.
Keywords: difference equations; difference; existence local; boundary conditions ... See more keywords
Gronwall's inequality for a nabla fractional difference system with a retarded argument and an application
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Difference Equations and Applications"
DOI: 10.1080/10236198.2019.1581180
Abstract: ABSTRACT We study the nabla fractional difference system with retarded argument. There are two major ingredients. A Gronwall's inequality for the nabla case is given. This allows us to evaluate the solution of nabla fractional… read more here.
Keywords: difference system; difference; fractional difference; nabla fractional ... See more keywords
Positive Solutions for a System of Semipositone Fractional Difference Boundary Value Problems
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DOI: 10.1155/2018/6835028
Abstract: Using the fixed point index, we establish two existence theorems for positive solutions to a system of semipositone fractional difference boundary value problems. We adopt nonnegative concave functions and nonnegative matrices to characterize the coupling… read more here.
Keywords: fractional difference; system semipositone; semipositone fractional; positive solutions ... See more keywords
On the oscillation of q-fractional difference equations
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DOI: 10.1186/s13662-017-1316-x
Abstract: AbstractIn this paper, sufficient conditions are established for the oscillation of solutions of q-fractional difference equations of the form {∇0αqx(t)+f1(t,x)=r(t)+f2(t,x),t>0,limt→0+qI0j−αx(t)=bj(j=1,2,…,m),$$ \left \{ \textstyle\begin{array}{l} {}_{q}\nabla_{0}^{\alpha}x(t)+f_{1}(t,x)=r(t)+f_{2}(t,x), \quad t>0 ,\\ \lim_{t \to0^{+}}{{}_{q}I_{0}^{j-\alpha}x(t)}=b_{j} \quad(j=1,2,\ldots,m), \end{array}\displaystyle \right . $$ where… read more here.
Keywords: difference equations; difference; equations oscillation; fractional difference ... See more keywords
Existence and Ulam stability for implicit fractional q-difference equations
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DOI: 10.1186/s13662-019-2411-y
Abstract: This paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and… read more here.
Keywords: difference equations; difference; fractional difference; equations existence ... See more keywords
Coupled implicit Caputo fractional q-difference systems
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DOI: 10.1186/s13662-019-2433-5
Abstract: This paper deals with some existence, uniqueness, and Ulam stability results for a coupled implicit Caputo fractional q-difference system in Banach and generalized Banach spaces. Some applications are made of some fixed point theorems for… read more here.
Keywords: difference; fractional difference; caputo fractional; implicit caputo ... See more keywords
Stability analysis by fixed point theorems for a class of non-linear Caputo nabla fractional difference equation
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DOI: 10.1186/s13662-020-02674-1
Abstract: Fractional difference equations have become important due to their qualitative properties and applications in discrete modeling. Stability analysis of solutions is one of the most widely used qualitative properties with tremendous applications. In this paper,… read more here.
Keywords: difference; fractional difference; analysis; stability ... See more keywords