Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 4Citation - Scopus: 6A Fractional Derivative Inclusion Problem Via an Integral Boundary Condition(Eudoxus Press, Llc, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Moghaddam, Mehdi; Mohammadi, Hakimeh; Rezapour, Shahram; MatematikWe investigate the existence of solutions for the fractional differential inclusion (c)D(alpha)x(t) is an element of F(t, x(t)) (equipped with the boundary value problems x(0) = 0 and x(1) = integral(eta)(0) x(s)ds, where 0 < eta < 1, 1 < alpha <= 2, D-c(alpha) is the standard Caputo differentiation and F : [0, 1] x R -> 2(R) is a compact valued multifunction. An illustrative example is also discussed.Article Citation - WoS: 117Citation - Scopus: 120A Novel Modeling of Boundary Value Problems on the Glucose Graph(Elsevier, 2021) Etemad, Sina; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruIn this article, with due attention to a new labeling method for vertices of arbitrary graphs, we investigate the existence results for a novel modeling of the fractional multi term boundary value problems on each edge of the graph representation of the Glucose molecule. In this direction, we consider a graph with labeled vertices by 0 or 1 inspired by the molecular structure of the Glucose molecule and then derive some existence results by applying two known fixed point theorems. Finally, we provide an example to illustrate the validity of our main result. (c) 2021 Elsevier B.V. All rights reserved.Article Citation - WoS: 716Citation - Scopus: 762A New Study on the Mathematical Modelling of Human Liver With Caputo-Fabrizio Fractional Derivative(Pergamon-elsevier Science Ltd, 2020) Jajarmi, Amin; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruIn this research, we aim to propose a new fractional model for human liver involving Caputo-Fabrizio derivative with the exponential kernel. Concerning the new model, the existence of a unique solution is explored by using the Picard-Lindelof approach and the fixed-point theory. In addition, the mathematical model is implemented by the homotopy analysis transform method whose convergence is also investigated. Eventually, numerical experiments are carried out to better illustrate the results. Comparative results with the real clinical data indicate the superiority of the new fractional model over the pre-existent integer-order model with ordinary time-derivatives. (C) 2020 Elsevier Ltd. All rights reserved.Article Citation - WoS: 66Citation - Scopus: 74Two Fractional Derivative Inclusion Problems Via Integral Boundary Condition(Elsevier Science inc, 2015) Baleanu, Dumitru; Hedayati, Vahid; Rezapour, Shahram; Agarwal, Ravi P.; Moghaddam, Mehdi; Mohammadi, HakimehThe goal of the manuscript is to analyze the existence of solutions for the Caputo fractional differential inclusion (c)D(q)x(t) is an element of F(t,x(t), (c)D(beta)x(t)) with the boundary value conditions x(0) = 0 and x(1) + x'(1) = integral(eta)(0) x(s)ds, such that 0 < eta < 1, 1 < q <= 2, 0 < beta < 1 and q = beta > 1. Also, we investigate the existence of solutions for the Caputo fractional differential inclusion (c)D(q)x(t) is an element of F(t,x(t)) such that x(0) = a integral(nu)(0) x(s)ds and x(1) = b integral(eta)(0) x(s)ds, where 0 < nu, eta < 1, 1 < q <= 2 and a, b is an element of R. (C) 2014 Elsevier Inc. All rights reserved.