Search

Fractional calculus provides some fractional operators for us to model different real-world phenomena mathematically. One of these important study fields is the mathematical model of the elastic beam changes. More precisely, in this paper, based on the behavior patterns of an elastic beam, we consider the generalized sequential boundary value problems of the Navier difference equations by using the post-quantum fractional derivatives of the Caputo-like type. We discuss on the existence theory for solutions of the mentioned (p ; q) -difference Navier problems in two single-valued and set-valued versions. We use the main properties of the (p ; q) -operators in this regard. Application of the fixed points of the ρ - θ -contractions along with the endpoints of the multi-valued functions play a fundamental role to prove the existence results. Finally in two examples, we validate our models and theoretical results by giving numerical models of the generalized sequential (p ; q) -difference Navier problems. [ABSTRACT FROM AUTHOR]

In this research study, we formulate two generalized nonlinear multi-order fractional boundary value problems with the help of quantum diffeerence operators. To investigate the exis- tence property for possible solutions of these q-di_erence FBVPs, we apply two separate methods motivated by some notions in relation to the measure of noncompactness and end-point technique. The condensing functions and multifunctions having the (AE)-property play an important role in our study. As well as, two examples corresponding to both techniques are provided to ensure the compatibility of the findings numerically. [ABSTRACT FROM AUTHOR]

The present research work investigates some new results for a fractional generalized Sturm–Liouville–Langevin (FGSLL) equation involving the Ψ-Caputo fractional derivative with a modified argument. We prove the uniqueness of the solution using the Banach contraction principle endowed with a norm of the Ψ-Bielecki-type. Meanwhile, the fixed-point theorems of the Leray–Schauder and Krasnoselskii type associated with the Ψ-Bielecki-type norm are used to derive the existence properties by removing some strong conditions. We use the generalized Gronwall-type inequality to discuss Ulam–Hyers (UH), generalized Ulam–Hyers (GUH), Ulam–Hyers–Rassias (UHR), and generalized Ulam–Hyers–Rassias (GUHR) stability of these solutions. Lastly, three examples are provided to show the effectiveness of our main results for different cases of (FGSLL)-problem such as Caputo-type Sturm–Liouville, Caputo-type Langevin, Caputo–Erdélyi–Kober-type Langevin problems. [ABSTRACT FROM AUTHOR]

In this paper, we provide some appropriate conditions for the existence of solutions for a perturbed fractional neutral integro-differential system under the deformable derivative in a Banach space. Using the Banach contraction principle and Krasnoselskii's fixed point theorem, we establish some new existence theorems. Moreover, we provide two numerical examples to demonstrate the applicability of the theoretical results [ABSTRACT FROM AUTHOR]

In this research, we introduce a new and generalized family of convex functions, entitled the α-convex functions in the second sense with respect to a parameter and examine their important algebraic properties. Based on this novel convexity concept, we explore a new class of fractional integral inequalities for functions that are twice differentiable. These results are derived from fundamental identities obtained using classical Riemann–Liouville fractional integrals. To validate our findings, we provide 2D and 3D graphs of the main results. Furthermore, as an additional aspect of our study, we explore error estimates for differences of generalized means. [ABSTRACT FROM AUTHOR]

Rapid emissions of green-house gases (GHGs) are causing global warming, which is wreaking havoc on the earth's climate system. As a result, the coastal ecosystems of the world are on the verge of becoming endangered. We develop a fractal-fractional hybrid model to estimate the influence of rapid emissions of GHGs on the coastal ecosystems and climate changes. The fractal-fractional climate change model is considered for the theoretical and numerical aspects. The theoretical aspect includes the existence and Hyers–Ulam (HU) stability of the solutions while the numerical aspect is based on Lagrange's interpolation polynomial. Moreover, unique solutions are proved by the Banach contraction principle. Different fractal-fractional orders are considered for the numerical study of dynamics of solutions which prove the importance and accuracy of these hybrid operators. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and stability of solutions in connection to a non-local multiterm boundary value problem (BVP) with differential equations equipped with the Riemann-Liouville (RL) fractional derivative in the sense of Atangana-Baleanu of variable-order. The results about the existence property are investigated and proved via Krasnoselskii's fixed point theorem. Note that all theorems in the present research are studied based on piece-wise constant functions defined on generalized intervals. We shall convert our main BVP with the RL-fractional derivative of the Atangana-Baleanu type of variable-order to an equivalent BVP of constant order of the RL-Atangana-Baleanu derivative. In the next step, we examine the Ulam-Hyers stability for the supposed variable-order RL-Atangana-Baleanu BVP. Finally, we provide some examples to validate that our results are applicable. [ABSTRACT FROM AUTHOR]

In this paper, a newfangled technique for edge detection that combines the Khalil conformable derivative and the Hessian matrix is developed and experimentally validated. The following main aspects are considered: (i) to attenuate image noise a Gaussian kernel inspired by the Khalil conformable derivative was developed. (ii) The spatial derivatives of the image gray level are calculated via the Khalil derivative, which is suitable for maintaining object contours and texture information even in low-contrast and resolution images. (iii) The conformable Hessian matrix is obtained from these image derivatives, generating continuous, thicker, and brighter edges. Our operator is compared with some existing techniques. Simulation results on different test images confirm a greater robustness to noise by our operator as well as a better visual quality of the edge maps obtained. This statement is validated through a comparative analysis based on peak signal-to-noise ratio and edge-strength-similarity-based image quality. In addition, it is applied in medical image processing and analysis tasks such as mammogram images, computed tomography scans, and magnetic resonance imaging for identification tasks of middle cerebral artery aneurysms, calcifications and breast cancer, proliferative Diabetic Retinopathy, and cerebral arteriovenous malformations. According to our findings, the conformable operator allows better visual identification of the structure of these conditions, improving the accuracy of clinical diagnosis and its subsequent monitoring. [ABSTRACT FROM AUTHOR]