An Alternative Approach for Nonlinear Optimization Problem with Caputo - Fabrizio Derivative

Abstract

In this study, a fractional mathematical model with steepest descent direction is proposed to find optimal solutions for a class of nonlinear programming problem. In this sense, Caputo-Fabrizio derivative is adapted to the mathematical model. To demonstrate the solution trajectory of the mathematical model, we use the multistage variational iteration method (MVIM). Numerical simulations and comparisons on some test problems show that the mathematical model generated using Caputo-Fabrizio fractional derivative is both feasible and efficient to find optimal solutions for a certain class of equality constrained optimization problems.

Analytical and numerical approaches to nerve impulse model of fractional‐order

“…In this subsection, we define the modified decomposition components constructed by the conformable operator for Equation (22). Taking the LT of both sides of Equation (22) and taking the fact that in Lemma 1, we get…”

“…Avci et al [15] explored a heat conduction equation with respect to the Caputo-Fabrizio fractional derivative. Many other fractional models have been treated with these fractional-order derivatives [16][17][18][19][20][21][22].…”

Characterizations of two different fractional operators without singular kernel

“…The other definition, which is defined by Yang et al [7] in 2017, is based on the normalized sinc function (NSFDO). Especially in recent years, many important theoretical results and applications have been obtained using an operator which has non-local and non-singular kernel such as the Caputo-Fabrizio, NSFDO and ABO [8][9][10][11][12][13][14][15][16][17][18]. Both of these operators have some illustrative advantages according to the operators defined previously such as Caputo [19] and conformable [20].…”

Calogero-Bogoyavlenskii-Schiff denkleminin analitik çözümleri

“…Bu denklemlerin çözümlerini elde etmek için nümerik ve analitik metotlar geliştirilmiştir [5]. Bu metotlardan; Varyasyonel İterasyon Metot [6,7], Homotopi Analiz Metot [8], Homotopi Pertürbasyon Metot [9][10][11], Adomian Ayrışım Metot [12], Homojen Denge Metot [13][14][15][16][17][18][19][20][21][22][23][24] ve diğerleri son yirmi yılda litaratürde bulunan çalışmalardandır. Lineer olmayan denklemlerin çözümlerine Homojen Denge Metodun kullanımıyla hızlı ve analitik sonuçlara ulaşılmaktadır.…”