Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 5Citation - Scopus: 12Non-Instantaneous Impulsive Fractional-Order Delay Differential Systems With Mittag-Leffler Kernel(Amer inst Mathematical Sciences-aims, 2022) Arjunan, Mani Mallika; Baleanu, Dumitru; Kavitha, VelusamyThe existence of fractional-order functional differential equations with non-instantaneous impulses within the Mittag-Leffler kernel is examined in this manuscript. Non-instantaneous impulses are involved in such equations and the solution semigroup is not compact in Banach spaces. We suppose that the nonlinear term fulfills a non-compactness measure criterion and a local growth constraint. We further assume that non-instantaneous impulsive functions satisfy specific Lipschitz criteria. Finally, an example is given to justify the theoretical results.Article Citation - WoS: 3Citation - Scopus: 3Fuzzy Fractional Estimates of Swift-Hohenberg Model Obtained Using the Atangana-Baleanu Fractional Derivative Operator(Amer inst Mathematical Sciences-aims, 2022) Sultana, Sobia; Kanwal, Bushra; Jarad, Fahd; Khalid, Aasma; Rashid, SaimaSwift-Hohenberg equations are frequently used to model the biological, physical and chemical processes that lead to pattern generation, and they can realistically represent the findings. This study evaluates the Elzaki Adomian decomposition method (EADM), which integrates a semi-analytical approach using a novel hybridized fuzzy integral transform and the Adomian decomposition method. Moreover, we employ this strategy to address the fractional-order Swift-Hohenberg model (SHM) assuming gH-differentiability by utilizing different initial requirements. The Elzaki transform is used to illustrate certain characteristics of the fuzzy Atangana-Baleanu operator in the Caputo framework. Furthermore, we determined the generic framework and analytical solutions by successfully testing cases in the series form of the systems under consideration. Using the synthesized strategy, we construct the approximate outcomes of the SHM with visualizations of the initial value issues by incorporating the fuzzy factor pi is an element of [0, 1] which encompasses the varying fractional values. Finally, the EADM is predicted to be e ffective and precise in generating the analytical results for dynamical fuzzy fractional partial di fferential equations that emerge in scientific disciplines.Article Citation - WoS: 8Citation - Scopus: 10Fractional-Order Partial Differential Equations Describing Propagation of Shallow Water Waves Depending on Power and Mittag-Leffier Memory(Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Sultana, Sobia; Jarad, Fahd; Alsharif, Abdullah M.; Al Qurashi, MaysaaIn this research, the (q) over bar -homotopy analysis transform method ((q) over bar -HATM) is employed to identify fractional-order Whitham-Broer-Kaup equation (WBKE) solutions. The WBKE is extensively employed to examine tsunami waves. With the aid of Caputo and Atangana-Baleanu fractional derivative operators, to obtain the analytical findings of WBKE, the predicted algorithm employs a combination of (q) over bar -HAM and the Aboodh transform. The fractional operators are applied in this work to show how important they are in generalizing the frameworks connected with kernels of singularity and non-singularity. To demonstrate the applicability of the suggested methodology, various relevant problems are solved. Graphical and tabular results are used to display and assess the findings of the suggested approach. In addition, the findings of our recommended approach were analyzed in relation to existing methods. The projected approach has fewer processing requirements and a better accuracy rate. Ultimately, the obtained results reveal that the improved strategy is both trustworthy and meticulous when it comes to assessing the influence of nonlinear systems of both integer and fractional order.Article Citation - WoS: 29Citation - Scopus: 27Fractional Physical Problems Including Wind-Influenced Projectile Motion With Mittag-Leffler Kernel(Amer inst Mathematical Sciences-aims, 2020) Bas, Erdal; Baleanu, Dumitru; Acay, Bahar; Ozarslan, RamazanIn this manuscript the fractional form of wind-influenced projectile motion equations which have a significant place in physics is extensively investigated by preserving dimensionality of the physical quantities for fractional operators and features of wind-influenced projectile motion are computed analytically in view of Atangana-Baleanu (ABC) fractional derivative in Caputo sense. Moreover, ABC fractional derivative with (n + alpha)th-order and its Laplace transform (LT) are obtained, alpha is an element of [0, 1] and n is an element of N. A comparative analysis based on the classical case is carried out in order to shed more light on the potent of the ABC fractional operator. Hence we present the results for some values of ff, k friction constant, different wind effects and different masses in 3D illustrations by comparing Caputo fractional operator. Thus, we can observe trajectory, time of flight, maximum height and range clearly. Moreover, the obtained results are shown to correspond to the classical case while the order alpha -> 1.Article Citation - WoS: 10Citation - Scopus: 10Existence of Local and Global Solutions To Fractional Order Fuzzy Delay Differential Equation With Non-Instantaneous Impulses(Amer inst Mathematical Sciences-aims, 2022) Malik, Muslim; Sajid, Mohammad; Baleanu, Dumitru; Kumar, AnilThe main concern of this manuscript is to examine some sufficient conditions under which the fractional order fuzzy delay differential system with the non-instantaneous impulsive condition has a unique solution. We also study the existence of a global solution for the considered system. Fuzzy set theory, Banach fixed point theorem and Non-linear functional analysis are the major tools to demonstrate our results. In last, an example is given to illustrate these analytical results.