In this manuscript, we study a class of equations with two different Riemann–Liouville-type orders nabla difference operators. We show some new and fundamental properties the related Green’s function. Depending on values operators, split our research into main cases, for each one them, obtain suitable conditions under which prove that considered problem possesses positive solution. consider latter to be novelty in work. Our tool both cases is Guo–Krasnoselskii’s fixed point theorem. end,...

In this paper, we consider a fourth-order three-point boundary value problem. Despite the fact that corresponding Green’s function changes its sign on square of definition, obtain existence at least one positive and decreasing solution under some suitable conditions. The results are based classical Krasosel’skii’s fixed point theorem in cones. Then, impose sufficient conditions allow us to deduce nonexistence results. end, examples given order illustrate our main

A difference equation is a relation between the differences of function at one or more general values independent variable. These equations usually describe evolution certain phenomena over course time. The present paper deals with existence and uniqueness solutions fractional equations.

We consider positivity, monotonicity, and convexity results for discrete fractional operators with exponential kernels. Our cover both the sequential nonsequential cases, we demonstrate similarities dissimilarities between kernel case differences other types of This shows that qualitative information gleaned in is not precisely same as cases.

This work provides new adequate conditions for difference equations with forcing, positive and negative terms to have non-oscillatory solutions. A few mathematical inequalities the properties of discrete fractional calculus serve as fundamental foundation our approach. To help establish main results, an analogous representation equation, called a Volterra-type summation is constructed. Two numerical examples are provided demonstrate validity theoretical findings; no earlier publications been...

This article discusses the existence of positive solutions to Sturm–Liouville boundary value problems for Riemann–Liouville nabla fractional difference equations. The results obtained here shall generalize existing ones. We provide a few examples illustrate applicability established results.

This paper continues the subject of symmetry breaking fractional-order maps, previously addressed by one authors. Several known planar classes curves integer order are considered and transformed into their fractional order. For this purpose, Grunwald–Letnikov numerical scheme is used. It shown numerically that aesthetic appeal most broken when variants. The defined parametric representation, Cartesian iterated function systems. To facilitate implementation, under affine representation. In...

In this paper, we study the coupled system of nonlinear Langevin equations involving Caputo–Hadamard fractional derivative and subject to nonperiodic boundary conditions. The existence, uniqueness, stability in sense Ulam are established for proposed system. Our approach is based on features Hadamard derivative, implementation fixed point theorems, employment Urs's approach. An example introduced facilitate understanding theoretical findings.

Abstract In this paper, we study a coupled system of generalized Sturm–Liouville problems and Langevin fractional differential equations described by Atangana–Baleanu–Caputo (ABC for short) derivatives whose formulations are based on the notable Mittag-Leffler kernel. Prior to main results, equivalence nonlinear integral is proved. Once that has been done, show in detail existence–uniqueness Ulam stability aid fixed point theorems. Further, continuous dependence solutions extensively...

<abstract> It is well known that Newton's second law can be applied in various biological processes including the behavior of vibrating eardrums. In this work, we consider a nonlinear discrete fractional initial value problem as model describing dynamic eardrum. We establish sufficient conditions for existence, uniqueness, and Hyers-Ulam stability solutions proposed model. To examine validity our findings, concrete example forced eardrum equation along with numerical simulation analyzed. </abstract>

This article is devoted to deduce the expression of Green's function related a general constant coefficients fractional difference equation coupled Dirichlet conditions. In this case, due points where some operators are applied, we in presence an implicit equation. So, such property, it more complicated calculate and manage than explicit case studied previous work authors. Contrary shown that constructed as finite sums, here infinite series. fact makes necessary impose restrictive...

This paper deals with fractional boundary value problems involving the Hilfer–Hadamard differential operator of order [Formula: see text] and type text]. We derive corresponding Lyapunov-type inequalities for two prominent classes (HFBVPs) separated anti-periodic conditions. For this purpose, we construct associated Green’s functions deduce their important properties.

In this paper, we study a class of nabla fractional difference equations with multipoint summation boundary conditions. We obtain the exact expression corresponding Green’s function and deduce some its properties. Then, impose sufficient conditions in order to ensure existence uniqueness results. Also, establish under which solution considered problem is generalized Ulam–Hyers–Rassias stable. end, examples are included illustrate our main

Abstract We consider the sequential CFC-type nabla fractional difference <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mo stretchy="false">(</m:mo> <m:mi>CFC</m:mi> </m:msup> <m:msubsup> <m:mo>∇</m:mo> <m:mi>a</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mi>ν</m:mi> </m:msubsup> <m:mmultiscripts> <m:mi>μ</m:mi> <m:mprescripts /> <m:none </m:mmultiscripts> <m:mi>u</m:mi> stretchy="false">)</m:mo> <m:mi>t</m:mi> </m:math>...

We investigate the Hyers-Ulam stability, generalized and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>-Hyers-Ulam stability of a linear fractional nabla difference equation using discrete Laplace transform. provide few examples to illustrate applicability established results.

In this article, we consider a family of two-point Riemann-Liouville type nabla fractional boundary value problems involving difference condition.We construct the corresponding Green's function and deduce its ordering property.Then, obtain Lyapunov-type inequality using properties function, illustrate few applications.

In this article, we consider a particular class of nabla fractional boundary value problems with general conditions, and establish sufficient conditions on existence uniqueness its solutions.

In this paper, we analyse periodic properties of fractional nabla difference systems.First, prove that a system equations with right hand side can not possess solution.Next, establish sufficient conditions on the existence unique S -asymptotically T -periodic solution for system.Finally, provide an example illustrating obtained results.