WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Publisher: search.filters.publisher.Amer inst Mathematical Sciences-aimsSubject: search.filters.subject.Fixed Point Theorem

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Now showing 1 - 9 of 9
  • Article
    Citation - WoS: 8
    Citation - Scopus: 8
    Qualitative Analysis of a Fuzzy Volterra-Fredholm Integrodifferential Equation With an Atangana-Baleanu Fractional Derivative
    (Amer inst Mathematical Sciences-aims, 2022) Shah, Kamal; Jarad, Fahd; Abdo, Mohammed S.; Abdeljawad, Thabet; Almalahi, Mohammed A.; Panchal, Satish K.
    The point of this work was to analyze and investigate the sufficient conditions of the existence and uniqueness of solutions for the nonlinear fuzzy fractional Volterra Fredholm integrodifferential equation in the frame of the Atangana-Baleanu-Caputo fractional derivative methodology. To begin with, we give the parametric interval form of the Atangana-Baleanu-Caputo fractional derivative on fuzzy set-valued functions. Then, by employing Schauder???s and Banach???s fixed point procedures, we examine the existence and uniqueness of solutions for fuzzy fractional Volterra Fredholm integro-differential equation with the Atangana-Baleanu-Caputo fractional operator. It turns out that the last interval model is a combined arrangement of nonlinear equations. In addition, we consider results by applying the Adams Bashforth fractional technique and present two examples that have been numerically solved using graphs.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 12
    Non-Instantaneous Impulsive Fractional-Order Delay Differential Systems With Mittag-Leffler Kernel
    (Amer inst Mathematical Sciences-aims, 2022) Arjunan, Mani Mallika; Baleanu, Dumitru; Kavitha, Velusamy
    The 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: 2
    Citation - Scopus: 2
    New Results for a Coupled System of Abr Fractional Differential Equations With Sub-Strip Boundary Conditions
    (Amer inst Mathematical Sciences-aims, 2022) Panchal, Satish K.; Aljaaidi, Tariq A.; Jarad, Fahd; Almalahi, Mohammed A.
    In this article, we investigate sufficient conditions for the existence, uniqueness and UlamHyers (UH) stability of solutions to a new system of nonlinear ABR fractional derivative of order 1 < e <= 2 subjected to multi-point sub-strip boundary conditions. We discuss the existence and uniqueness of solutions with the assistance of Leray-Schauder alternative theorem and Banach's contraction principle. In addition, by using some mathematical techniques, we examine the stability results of Ulam-Hyers (UH). Finally, we provide one example in order to show the validity of our results.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 17
    Approximation of Solutions for Nonlinear Functional Integral Equations
    (Amer inst Mathematical Sciences-aims, 2022) Pathak, Vijai Kumar; Baleanu, Dumitru; Mishra, Lakshmi Narayan
    In this article, we consider a class of nonlinear functional integral equations, motivated by an equation that offers increasing evidence to the extant literature through replication studies. We investigate the existence of solution for nonlinear functional integral equations on Banach space C[0, 1]. We use the technique of the generalized Darbo's fixed-point theorem associated with the measure of noncompactness (MNC) to prove our existence result. Also, we have given two examples of the applicability of established existence result in the theory of functional integral equations. Further, we construct an efficient iterative algorithm to compute the solution of the first example, by employing the modified homotopy perturbation (MHP) method associated with Adomian decomposition. Moreover, the condition of convergence and an upper bound of errors are presented.
  • Article
    Citation - WoS: 13
    Citation - Scopus: 16
    Existence, Uniqueness and Stability of Solutions for Generalized Proportional Fractional Hybrid Integro-Differential Equations With Dirichlet Boundary Conditions
    (Amer inst Mathematical Sciences-aims, 2022) Jarad, Fahd; Laadjal, Zaid
    In this work, the existence of solutions for nonlinear hybrid fractional integro-differential equations involving generalized proportional fractional (GPF) derivative of Caputo-Liouville-type and multi-term of GPF integrals of Reimann-Liouville type with Dirichlet boundary conditions is investigated. The analysis is accomplished with the aid of the Dhage's fixed point theorem with three operators and the lower regularized incomplete gamma function. Further, the uniqueness of solutions and their Ulam-Hyers-Rassias stability to a special case of the suggested hybrid problem are discussed. For the sake of corroborating the obtained results, an illustrative example is presented.
  • Article
    Citation - WoS: 31
    Citation - Scopus: 34
    An E Ffective Method for Solving Nonlinear Integral Equations Involving the Riemann-Liouville Fractional Operator
    (Amer inst Mathematical Sciences-aims, 2023) Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; Paul, Supriya Kumar
    In this paper, under some conditions in the Banach space C([0; beta];R), we establish the existence and uniqueness of the solution for the nonlinear integral equations involving the Riemann-Liouville fractional operator (RLFO). To establish the requirements for the existence and uniqueness of solutions, we apply the Leray-Schauder alternative and Banach's fixed point theorem. We analyze Hyers-Ulam-Rassias (H-U-R) and Hyers-Ulam (H-U) stability for the considered integral equations involving the RLFO in the space C([0; beta];R). Also, we propose an e ffective and e fficient computational method based on Laguerre polynomials to get the approximate numerical solutions of integral equations involving the RLFO. Five examples are given to interpret the method.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 10
    Existence 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, Anil
    The 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: 39
    Existence and Uniqueness of Miscible Flow Equation Through Porous Media With a Non Singular Fractional Derivative
    (Amer inst Mathematical Sciences-aims, 2020) Yadav, Mahaveer Prasad; Baleanu, Dumitru; Purohit, S. D.; Agarwal, Ritu
    In this paper, we discuss the phenomenon of miscible flow with longitudinal dispersion in porous media. This process simultaneously occur because of molecular diffusion and convection. Here, we analyze the governing differential equation involving Caputo-Fabrizio fractional derivative operator having non singular kernel. Fixed point theorem has been used to prove the uniqueness and existence of the solution of governing differential equation. We apply Laplace transform and use technique of iterative method to obtain the solution. Few applications of the main result are discussed by taking different initial conditions to observe the effect on derivatives of different fractional order on the concentration of miscible fluids.
  • Article
    Citation - WoS: 102
    Citation - Scopus: 120
    A Fractional Model for the Dynamics of Tuberculosis Infection Using Caputo-Fabrizio Derivative
    (Amer inst Mathematical Sciences-aims, 2020) Khan, Muhammad Altaf; Farooq, Muhammad; Hammouch, Zakia; Baleanu, Dumitru; Ullah, Saif
    In the present paper, we study the dynamics of tuberculosis model using fractional order derivative in Caputo-Fabrizio sense. The number of confirmed notified cases reported by national TB program Khyber Pakhtunkhwa, Pakistan, from the year 2002 to 2017 are used for our analysis and estimation of the model biological parameters. The threshold quantity R-0 and equilibria of the model are determined. We prove the existence of the solution via fixed-point theory and further examine the uniqueness of the model variables. An iterative solution of the model is computed using fractional Adams-Bashforth technique. Finally, the numerical results are presented by using the estimated values of model parameters to justify the significance of the arbitrary fractional order derivative. The graphical results show that the fractional model of TB in Caputo-Fabrizio sense gives useful information about the complexity of the model and one can get reliable information about the model at any integer or non-integer case.