Mathematical and Theoretical Analysis

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In this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary…

ABSTRACT In statistics, samples are drawn from a population in a data‐generating process (DGP). Standard errors measure the uncertainty in estimates of population parameters. In science, evidence is generated to test hypotheses in an evidence‐generating process (EGP). We claim that EGP variation across researchers add…

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• MUHAMMED KURULAY

A new concept of quasi slowly oscillating continuity is introduced. Furthermore, it is shown that this kind of continuity implies ordinary continuity, but the converse is not always true.

• İBRAHİM ÇANAK

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• ALİ UZER

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• ALİ AKGÜL

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• ALİ AKGÜL

It is known that Laplace transform converges for functions of exponential order. Inorder to extend the possibility of working in a large class of functions, we present a modied Laplacetransform that we call \\rho-Laplace transform, study its properties and prove its own convolution the-orem. Then, we apply it to solve…

One of the flash analytic approximate methods of nowadays for the solution of highly nonlinear algebraic or differential equations arising from the mathematical modelling of industrial and technological applications is the homotopy analysis method (HAM). The success of the HAM is mainly due to a so-called convergence…

• MUSTAFA TÜRKYILMAZOĞLU

The fractional variational principles within Riemann–Liouville fractional derivatives in the presence of delay are analyzed. The corresponding Euler–Lagrange equations are obtained and one example is analyzed in detail.

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• AHMET YILDIRIM