WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 10Citation - Scopus: 11Novel Numerical Investigation of the Fractional Oncolytic Effectiveness Model With M1 Virus Via Generalized Fractional Derivative With Optimal Criterion(Elsevier, 2022) Khalid, Aasma; Sultana, Sobia; Jarad, Fahd; Abualnaja, Khadijah M.; Hamed, Y. S.; Rashid, SaimaOncolytic virotherapy is an efficacious chemotherapeutic agent that addresses and eliminates cancerous tissues by employing recombinant infections. M1 is a spontaneously produced oncolytic alphavirus with exceptional specificity and powerful activity in individual malignancies. The objective of this paper is to develop and assess a novel fractional differential equation (FDEs)-based mathematical formalism that captures the mechanisms of oncogenic M1 immunotherapy. The aforesaid framework is demonstrated with the aid of persistence, originality, non-negativity, and stability of systems. Additionally, we also examine all conceivable steady states and the requirements that must exist for them to occur. We also investigate the global stability of these equilibria and the characteristics that induce them to be unstable. Furthermore, the Atangana- Baleanu fractional-order derivative is employed to generalize a treatment of the cancer model. This novel type of derivative furnishes us with vital understanding regarding parameters that are widely used in intricate mechanisms. The Picard-Lindelof approach is implemented to investigate the existence and uniqueness of solutions for the fractional cancer treatment system, and Picard's stability approach is used to address governing equations. The findings reveal that the system is more accurate when the fractional derivative is implemented, demonstrating that the behaviour of the cancer treatment can be interpreted when non-local phenomena are included in the system. Furthermore, numerical results for various configurations of the system are provided to exemplify the established simulation.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.Article Citation - WoS: 7Citation - Scopus: 9Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators(Mdpi, 2020) Darzi, Rahmat; Agheli, Bahram; Baleanu, DumitruA new form of nonlinear Langevin equation (NLE), featuring two derivatives of non-integer orders, is studied in this research. An existence conclusion due to the nonlinear alternative of Leray-Schauder type (LSN) for the solution is offered first and, following that, the uniqueness of solution using Banach contraction principle (BCP) is demonstrated. Eventually, the derivatives of non-integer orders are elaborated in Atangana-Baleanu sense.Article Citation - WoS: 108Citation - Scopus: 122A New Analysis of Fractional Fish Farm Model Associated With Mittag-Leffler Kernel(World Scientific Publ Co Pte Ltd, 2020) Kumar, Devendra; Baleanu, Dumitru; Singh, JagdevIn this paper, we analyze the dynamical behavior of fish farm model related to Atangana-Baleanu derivative of arbitrary order. The model is constituted with the group of non-linear differential equations having nutrients, fish and mussel. We have included discrete kind gestational delay of fish. The solution of fish farm model is determined by employing homotopy analysis transforms method (HATM). Existence of and uniqueness of solution are studied through Picard-Lindelof approach. The influence of order of new non-integer order derivative on nutrients, fish and mussel is discussed. The complete study reveals that the outer food supplies manage the behavior of the model. Moreover, to show the outcomes of the study, some numerical results are demonstrated through graphs.Article Citation - WoS: 85Citation - Scopus: 104Optimal Control for a Fractional Tuberculosis Infection Model Including the Impact of Diabetes and Resistant Strains(Elsevier Science Bv, 2019) AL-Mekhlafi, S. M.; Baleanu, D.; Sweilam, N. H.The objective of this paper is to study the optimal control problem for the fractional tuberculosis (TB) infection model including the impact of diabetes and resistant strains. The governed model consists of 14 fractional-order (FO) equations. Four control variables are presented to minimize the cost of interventions. The fractional derivative is defined in the Atangana-Baleanu-Caputo (ABC) sense. New numerical schemes for simulating a FO optimal system with Mittag-Leffler kernels are presented. These schemes are based on the fundamental theorem of fractional calculus and Lagrange polynomial interpolation. We introduce a simple modification of the step size in the two-step Lagrange polynomial interpolation to obtain stability in a larger region. Moreover, necessary and sufficient conditions for the control problem are considered. Some numerical simulations are given to validate the theoretical results. (C) 2019 The Authors. Published by Elsevier B.V. on behalf of Cairo University.Article Citation - WoS: 51Citation - Scopus: 88Chaos in a Cancer Model Via Fractional Derivatives With Exponential Decay and Mittag-Leffler Law(Mdpi, 2017) Guadalupe Lopez-Lopez, Maria; Manuel Alvarado-Martinez, Victor; Baleanu, Dumitru; Khan, Hasib; Francisco Gomez-Aguilar, Jose; Alvarado-Martínez, Victor Manuel; Gómez-Aguilar, José Francisco; López-López, María GuadalupeIn this paper, a three-dimensional cancer model was considered using the Caputo-Fabrizio-Caputo and the new fractional derivative with Mittag-Leffler kernel in Liouville-Caputo sense. Special solutions using an iterative scheme via Laplace transform, Sumudu-Picard integration method and Adams-Moulton rule were obtained. We studied the uniqueness and existence of the solutions. Novel chaotic attractors with total order less than three are obtained.