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and Applied Analysis 3 4. Solution by Homotopy Perturbation Sumudu Transform Method (HPSTM) 4.1. Basic Idea of HPSTM. To illustrate the basic idea of this method, we consider a general fractional nonlinear nonhomogeneous partial differential equationwith the initial condition of the form D α t U (x, t) + RU (x, t) + NU (x, t) = g (x, t) , (11) U (x, 0) = f… (More)

- Gholamreza Zabandan, Abasalt Bodaghi, Adem Kılıçman
- 2012

is known as the Hermite-Hadamard inequality (see [] for more information). Since then, some refinements of the Hermite-Hadamard inequality on convex functions have been extensively investigated by a number of authors (e.g., [, ] and []). In [], the first author obtained a new refinement of the Hermite-Hadamard inequality for convex functions.… (More)

and Applied Analysis 3 Proof. Let ξ be fixed. If φ t is in S, then its diffraction Fresnel transform certainly exists. Moreover, differentiating the right-hand side of 2.3 with respect to ξ, under the integral sign, ktimes, yields a sum of polynomials, pk t ξ , say of combinations of t and ξ. That is, ∣ ∣ ∣ ∣ ∣ d dtk Fd ( φ ) ξ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ pk t ξ φ… (More)

In this work we introduce some relationship between Sumudu and Laplace transforms, further; for the comparison purpose, we apply both transforms to solve differential equations to see the differences and similarities. Finally, we provide some examples regarding to second order differential equations with non constant coefficients as special case.… (More)

- Fazlollah Soleymani, Mahdi Sharifi, Solat Karimi Vanani, Farhad Khaksar Haghani, Adem Kılıçman
- TheScientificWorldJournal
- 2014

A new iterative scheme has been constructed for finding minimal solution of a rational matrix equation of the form X + A*X (-1) A = I. The new method is inversion-free per computing step. The convergence of the method has been studied and tested via numerical experiments.

- Zainab E. Abdulnaby, Rabha W. Ibrahim, Adem Kılıçman
- SpringerPlus
- 2016

Recently, the study of the fractional formal (operators, polynomials and classes of special functions) has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator [Formula: see text] defined by a fractional formal (fractional differential operator) and… (More)

We will introduce and study the pairwise weakly regular-Lindelöf bitopological spaces and obtain some results. Furthermore, we study the pairwise weakly regular-Lindelöf subspaces and subsets, and investigate some of their characterizations. We also show that a pairwise weakly regularLindelöf property is not a hereditary property. Some counterexamples will… (More)

In this study we extend the classification of partial differential equations to the further using the convolutions products. The purpose of this study is to compute the solutions of some explicit initial-boundary value problems for one-dimensional wave equation with variable coefficients by means of Laplace transform which in general has no solution.

- Assia Guezane-Lakoud, Rabah Khaldi, Adem Kılıçman
- SpringerPlus
- 2016

This paper concerns the solvability of a nonlinear fractional boundary value problem at resonance. By using fixed point theorems we prove that the perturbed problem has a solution, then by some ideas from analysis we show that the original problem is solvable. An example is given to illustrate the obatined results.

- Adem Kılıçman, Omer Altun
- 2014

In this work we study fractional order Sumudu transform. In the development of the definition we use fractional analysis based on the modified Riemann Liouville derivative, then we name the fractional Sumudu transform. We also establish a relationship between fractional Laplace and Sumudu via duality with complex inversion formula for fractional Sumudu… (More)