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Publisher : Hindawi Publishing C ... ✕Department : Uygulamalı Matematik ... ✕
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Exponentially Convex Functions on the Coordinates and Novel Estimations via Riemann-Liouville Fractional Operator

Ercan ÇELİK

In this study, the modification of the concept of exponentially convex function, which is a general version of convex functions, given on the coordinates, is recalled. With the help of an integral identity which includes the Riemann-Liouville (RL) fractional integral operator, new Hadamard-type inequalities are proved for exponentially convex functions on the coordinates. Many special cases of the results are discussed. Keywords: hadamard-type inequalities; rectangle

Article 2023 Fen Fakültesi Journal of Function Spaces2023 48 Views
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The Consecutive Substitution Method for Boundary Value Problems (BVPs) with Retarded Argument

Ercan ÇELİK

In this study, we applied an approximate solution method for solving the boundary value problems (BVPs) with retarded argument. The method is the consecutive substitution method. The consecutive substitution method was applied and an approximate solution was obtained. The numerical solution and the analytical solution are compared in the table. The solutions were found to be compatible. Keywords: approximate solution; boundary-value problem; numerical solution; retarded argument; solution methods; substitution method; boundary value problems

Article 2023 Fen Fakültesi Journal of Applied Mathematics2023 71 Views
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Invariant Solutions and Conservation Laws of the Time-Fractional Telegraph Equation

Ercan ÇELİK

In this study, the Lie symmetry analysis is given for the time-fractional telegraph equation with the Riemann-Liouville derivative. This equation is useable to describe the physical processes of models possessing memory. By applying classical and nonclassical Lie symmetry analysis for the telegraph equation with & alpha;,& beta; time-fractional derivatives and some technical computations, new infinitesimal generators are obtained. The actual methods give some classical symmetries while the nonclassical approach will bring back other symmetries to these equations. The similarity reduction and c ...More

Article 2023 Fen Fakültesi Advances in Mathematical Physics2023 14 Views
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Well-Posedness and Blow-Up of Solutions for a Variable Exponent Nonlinear Petrovsky Equation

Ercan ÇELİK

In this article, we investigate a nonlinear Petrovsky equation with variable exponent and damping terms. First, we establish the local existence using the Faedo-Galerkin approximation method under the conditions of positive initial energy and appropriate constraints on the variable exponents p & sdot; and q & sdot;. Finally, we prove a finite-time blow-up result for negative initial energy. Keyword: global existence; wave-equation

Article 2023 Fen Fakültesi Advances in Mathematical Physics2023 18 Views
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Existence, Decay, and Blow-up of Solutions for a Weighted m -Biharmonic Equation with Nonlinear Damping and Source Terms

Ercan ÇELİK

In this paper, we consider the weighted m-biharmonic equation with nonlinear damping and source terms. We proved the global existence of solutions. Later, the decay of the energy is established by using Nakao's inequality. Finally, we proved the blow-up of solutions in finite time.

Article 2024 Fen Fakültesi Journal of Function Spaces2024 12 Views
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