Fractional Differential Equations Solutions

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• THABET ABDELJAWAD

This manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these operators.

• EKİN UĞURLU

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• İBRAHİM ÖZKOL

Abstract Generalization of fractional differential operators was subjected to an intense debate in the last few years in order to contribute to a deep understanding of the behavior of complex systems with memory effect. In this article, a Caputo-type modification of Hadamard fractional derivatives is introduced. The p…

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• HÜSEYİN HAKLI

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• HARUN UĞUZ

We consider a one-dimensional fractional diffusion equation: ∂ α t u(x, t) = ∂ ∂x p(x) ∂u ∂x (x, t) , 0 < x < ℓ, where 0 < α < 1 and ∂ α t denotes the Caputo derivative in time of order α.We attach the homogeneous Neumann boundary condition at x = 0, ℓ and the initial value given by the Dirac delta function.We prove t…

• MASAHİRO YAMAMOTO

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• TOFIGH ALLAHVIRANLOU

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• TOFIGH ALLAHVIRANLOU

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…

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• SEVGİ ŞENGÜL AYAN