Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
31 results
Search Results
Article Citation - WoS: 14Citation - Scopus: 14Boundary Value Problem of Weighted Fractional Derivative of a Function With a Respect To Another Function of Variable Order(Springer, 2023) Jarad, Fahd; Alqudah, Manar A.; Abdeljawad, Thabet; Benia, Kheireddine; Souid, Mohammed SaidThis study aims to resolve weighted fractional operators of variable order in specific spaces. We establish an investigation on a boundary value problem of weighted fractional derivative of one function with respect to another variable order function. It is essential to keep in mind that the symmetry of a transformation for differential equations is connected to local solvability, which is synonymous with the existence of solutions. As a consequence, existence requirements for weighted fractional derivative of a function with respect to another function of constant order are necessary. Moreover, the stability with in Ulam-Hyers-Rassias sense is reviewed. The outcomes are derived using the Kuratowski measure of non-compactness. A model illustrates the trustworthiness of the observed results.Article Citation - WoS: 26Citation - Scopus: 31Analysis of Mixed Type Nonlinear Volterra-Fredholm Integral Equations Involving the Erdelyi-Kober Fractional Operator(Elsevier, 2023) Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; Paul, Supriya KumarThis paper investigates the existence, uniqueness and stability of solutions to the nonlinear Volterra-Fredholm integral equations (NVFIE) involving the Erdelyi-Kober (E-K) fractional integral operator. We use the Leray- Schauder alternative and Banach's fixed point theorem to examine the existence and uniqueness of solutions, and we also explore Hyers-Ulam (H-U) and Hyers-Ulam-Rassias (H-U-R) stability in the space C([0, fl], R). Furthermore, three solution sets U-sigma,U-lambda, U-theta,U-1 and U-1,U-1 are constructed for sigma > 0, lambda > 0, and theta is an element of (0,1), and then we obtain local stability of the solutions with some ideal conditions and by using Schauder fixed point theorem on these three sets, respectively. Also, to achieve the goal, we choose the parameters for the NVFIE as delta is an element of (1/2, 1), p is an element of (0,1), gamma > 0. Three examples are provided to clarify the results.Article An e ffective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator(2023) Paul, Supriya Kumar; Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, DumitruIn 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: 8Citation - Scopus: 8Qualitative 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: 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: 2Citation - Scopus: 2New 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: 5A New Existence Results on Fractional Differential Inclusions With State-Dependent Delay and Mittag-Leffler Kernel in Banach Space(Ovidius Univ Press, 2022) Kavitha, Velusamy; Baleanu, Dumitru; Arjunan, Mani MallikaIn this manuscript the existence of the fractional-order functional differential inclusions [FFDI] with state-dependent delay [SDD] is investigated within the Mittag-Leffler kernel. We use both contractive and condensing maps to prove the existence of mild solutions through solution operator. Finally, an example is presented to illustrate the theoretical findings.Article Citation - WoS: 15Citation - Scopus: 17Approximation of Solutions for Nonlinear Functional Integral Equations(Amer inst Mathematical Sciences-aims, 2022) Pathak, Vijai Kumar; Baleanu, Dumitru; Mishra, Lakshmi NarayanIn 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: 13Citation - Scopus: 16Existence, 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, ZaidIn 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: 31Citation - Scopus: 34An 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 KumarIn 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.