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Sunil Kumar Surath Ghosh Bessem Samet Emile Franc Doungmo Goufo 《Mathematical Methods in the Applied Sciences》2020,43(9):6062-6080
The heat equation is parabolic partial differential equation and occurs in the characterization of diffusion progress. In the present work, a new fractional operator based on the Rabotnov fractional-exponential kernel is considered. Next, we conferred some fascinating and original properties of nominated new fractional derivative with some integral transform operators where all results are significant. The fundamental target of the proposed work is to solve the multidimensional heat equations of arbitrary order by using analytical approach homotopy perturbation transform method and residual power series method, where new fractional operator has been taken in new Yang-Abdel-Aty-Cattani (YAC) sense. The obtained results indicate that solution converges to the original solution in language of generalized Mittag-Leffler function. Three numerical examples are discussed to draw an effective attention to reveal the proficiency and adaptability of the recommended methods on new YAC operator. 相似文献
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We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces.Presented theorems generalize recent results of Gordji et... 相似文献
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In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings. 相似文献
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Bessem Samet 《The European physical journal. Special topics》2017,226(16-18):3513-3524
We provide sufficient conditions for the non-existence of global solutions for a certain class of sequential fractional differential inequalities involving Riemann-Liouville left-sided fractional derivatives with different orders. To the best of our knowledge, the study of non-existence of solutions for fractional differential problems with sequential fractional derivatives has not been investigated until now. Our approach is based on the test function method. 相似文献
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Mohamed Jleli Mokhtar Kirane Bessem Samet 《Mathematical Methods in the Applied Sciences》2019,42(1):137-160
In this paper, we propose a new concept of derivative with respect to an arbitrary kernel function. Several properties related to this new operator, like inversion rules and integration by parts, are studied. In particular, we introduce the notion of conjugate kernels, which will be useful to guaranty that the proposed derivative operator admits a right inverse. The proposed concept includes as special cases Riemann‐Liouville fractional derivatives, Hadamard fractional derivatives, and many other fractional operators. Moreover, using our concept, new fractional operators involving certain special functions are introduced, and some of their properties are studied. Finally, an existence result for a boundary value problem involving the introduced derivative operator is proved. 相似文献
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We consider the following system of fractional differential equations where is the Riemann‐Liouville fractional derivative of order α,f,g : [0,1] × [0, ∞ ) × [0, ∞ ) → [0, ∞ ). Sufficient conditions are provided for the existence of positive solutions to the considered problem. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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We establish fixed point theorems for mixed monotone operators of Meir-Keeler type on ordered Banach spaces through projective metric. As applications, we use the fixed point theorems obtained in this paper to study the existence and uniqueness of positive solutions for different classes of nonlinear problems which include two-order two-point boundary value problems and fourth-order two-point boundary value problems for elastic beam equations. 相似文献
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