Nonlocal Cauchy Problem via a Fractional Operator Involving Power Kernel in Banach Spaces

Keten, Ayşegül; Yavuz, Mehmet; Băleanu, Dumitru

doi:10.3390/fractalfract3020027

Cited by 47 publications

(18 citation statements)

References 37 publications

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“…In consequence, this has led to different structures of arbitrary order differential equations formulated by several fractional operators. However, it has been understood that the most efficient procedure to discuss such a variety of fractional operators is to accommodate generalized structures of fractional operators that involve many other operators (see [8][9][10][11][12]).…”

Section: Introductionmentioning

confidence: 99%

On the Hybrid Fractional Differential Equations with Fractional Proportional Derivatives of a Function with Respect to a Certain Function

Abbas

Ragusa

2021

Symmetry

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This paper deals with a new class of hybrid fractional differential equations with fractional proportional derivatives of a function with respect to a certain continuously differentiable and increasing function ϑ. By means of a hybrid fixed point theorem for a product of two operators, an existence result is proved. Furthermore, the sufficient conditions of the continuous dependence on the given parameters are investigated. Finally, a simulative example is given to highlight the acquired outcomes.

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Section: Introductionmentioning

confidence: 99%

On the Hybrid Fractional Differential Equations with Fractional Proportional Derivatives of a Function with Respect to a Certain Function

Abbas

Ragusa

2021

Symmetry

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“…ere are several operators studied in the field of fractional calculus, for example, see [21][22][23][24][25][26], but the difference in this work is that the operator considered is in the sense of Caputo derivative.…”

Section: Introductionmentioning

confidence: 99%

A Nonlinear Implicit Fractional Equation with Caputo Derivative

Ndiaye

2021

Journal of Mathematics

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In this paper, we study a nonlinear implicit differential equation with initial conditions. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of Banach principle. Then, another result that deals with the existence of at least one solution is delivered and some sufficient conditions for this result are established by means of the fixed point theorem of Schaefer. At the end, we discuss two examples to illustrate the applicability of the main results.

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“…The concept and theory of fractional differential and integral operators are widely used to model many real‐word problems and physical mechanisms. Further, it aids us to capture some essential and important consequences and more information about the corresponding phenomena 7–27 . There are diverse definitions and notions for the differential and integral operators of noninteger order.…”

Section: Introductionmentioning

confidence: 99%

New approach for fractional Schrödinger‐Boussinesq equations with Mittag‐Leffler kernel

Prakasha

Malagi

Veeresha

2020

Math Methods in App Sciences

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In this paper, we find the solution and analyse the behaviour of the obtained results for the nonlinear Schrödinger-Boussinesq equations using q-homotopy analysis transform method (q-HATM) within the frame of fractional order. The considered system describes the interfaces between intermediate long and short waves. The projected fractional operator is proposed with the help of Mittag-Leffler function to incorporate the nonsingular kernel to the system. The projected algorithm is a modified and accurate method with the help of Laplace transform. The convergence analysis is presented with the help of the fixed point theorem in the form existence and uniqueness. To validate and illustrate the effectiveness of the algorithm considered, we exemplified considered system with respect of arbitrary order. Further, the behaviour of achieved results is captured in contour and 3D plots for distinct arbitrary order. The results show that the projected scheme is very effective, highly methodical and easy to apply for complex and nonlinear systems and help us to captured associated behaviour diverse classes of the phenomenon.

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Nonlocal Cauchy Problem via a Fractional Operator Involving Power Kernel in Banach Spaces

Cited by 47 publications

References 37 publications

On the Hybrid Fractional Differential Equations with Fractional Proportional Derivatives of a Function with Respect to a Certain Function

On the Hybrid Fractional Differential Equations with Fractional Proportional Derivatives of a Function with Respect to a Certain Function

A Nonlinear Implicit Fractional Equation with Caputo Derivative

New approach for fractional Schrödinger‐Boussinesq equations with Mittag‐Leffler kernel

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