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An Innovative Approach to Nonlinear Fractional Shock Wave Equations Using Two Numerical Methods
Mathematics, 2023 In this research, we propose a combined approach to solving nonlinear fractional shock wave equations using an Elzaki transform, the homotopy perturbation method, and the Adomian decomposition method. The nonlinear fractional shock wave equation is first
Meshari Alesemi
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A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws [PDF]
Advances in Difference Equations, 2021 AbstractIn this study, we investigate a new fourth-order integrable nonlinear equation. Firstly, by means of the efficient Hirota bilinear approach, we establish novel types of solutions which include breather, rogue, and three-wave solutions. Secondly, with the aid of Lie symmetry method, we report the invariance properties of the studied equation ...
Dumitru Baleanu +2 more
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Using analytical methods for finding the approximate solutions to fractional differential equations
International Journal of Thermofluids, 2023 This essay focuses on studying the nonlinear fractional integral equation. Various methods, including Akbari-Ganji's Method (AGM), Homotopy Perturbation Method (HPM), and Vibrational Iteration Method (VIM), are utilized to obtain its solution.
Reza Iranmanesh +7 more
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Pramana, 2023 In this paper, we present a method of deriving extended Prelle-Singer method's quantifiers from Darboux Polynomials for third-order nonlinear ordinary differential equations. By knowing the Darboux polynomials and its cofactors, we extract the extended Prelle-Singer method's quantities without evaluating the Prelle-Singer method's determining equations.
R Mohanasubha, M Senthilvelan
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Journal of Function Spaces, 2023 In the present paper, a new efficient technique is described for solving nonlinear mixed partial integrodifferential equations with continuous kernels.
Abeer M. Al-Bugami +2 more
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An Integral Equation Formulation for Two-Phase Flow and Other Nonlinear Flow Problems Through Porous Media [PDF]
SPE Annual Technical Conference and Exhibition, 1990 ABSTRACT Many flow problems encountered in petroleum reservoir engineering are characterized by nonlinearities and are difficult to solve analytically. The concept of a relative mass flow rate function is used to arrive at an integral equation formulation for some of these nonlinear flow problems.
Chen, Z. +2 more
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Mathematics, 2020 This study addresses the free vibration analysis of nonlinear structural-acoustic system with non-rigid boundaries. In practice, the boundaries of a panel–cavity system are usually imperfectly rigid.
Yiu-yin Lee
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Advances in Difference Equations, 2021 This research aims to investigate a novel coincidence point (cp) of generalized multivalued contraction (gmc) mapping involved a directed graph in b-metric spaces (b-ms).
Hasanen A. Hammad +2 more
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Three new approaches for solving a class of strongly nonlinear two-point boundary value problems
Boundary Value Problems, 2021 Three new and applicable approaches based on quasi-linearization technique, wavelet-homotopy analysis method, spectral methods, and converting two-point boundary value problem to Fredholm–Urysohn integral equation are proposed for solving a special case ...
Monireh Nosrati Sahlan, Hojjat Afshari
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Existence of solutions for a class of nonlinear Volterra integro-dynamic equations on time scales [PDF]
Arab Journal of Mathematical SciencesPurposeThis paper encompasses recent developments on a class of nonlinear Volterra integro-dynamic equations on arbitrary time scales. More precisely, we provide some conditions under which the considered equations have at least one, at least two and at ...
Svetlin Georgiev, Youssef N. Raffoul
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