Non-existence of Global Solutions for a Generalized Fractional Differential Problem [PDF]
arXiv, 2018 Aim of this paper is to study the non-existence of global solutions of the fractional differential problem involving generalized Katugampola derivative. We utilize the test function method and fractional integration by parts formula to obtain the result. An illustrative example is also given.
arxiv
Hermite-Hadamard's Mid-Point Type Inequalities for Generalized Fractional Integrals [PDF]
arXiv, 2019 Some Hermite-Hadamard's mid-point type inequalities related to Katugampola fractional integrals are obtained where the first derivative of considered mappings is Lipschitzian or convex. Also some mid-point type inequalities are given for Lipschitzian mappings, with the aim of generalizing the results presented in previous works.
arxiv
Study of Results of Katugampola Fractional Derivative and Chebyshev Inequailities. [PDF]
Int J Appl Comput Math, 2022 Nazeer N, Asjad MI, Azam MK, Akgül A.
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Ostrowski-type fractional integral inequalities for mappings whose derivatives are h-convex via Katugampola fractional integrals [PDF]
, 2018 Ghulam Farid +2 more
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On weighted fractional inequalities using generalized Katugampola fractional integral operator [PDF]
, 2020 Satish K. Panchal +2 more
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Fractional differential equations with dependence on the Caputo-Katugampola derivative [PDF]
arXiv, 2016 In this paper we present a new type of fractional operator, the Caputo-Katugampola derivative. The Caputo and the Caputo-Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy type problem, with dependence on the Caputo--Katugampola derivative, is proven.
arxiv
Existence and Stability of Fractional Differential Equations Involving Generalized Katugampola Derivative [PDF]
arXiv, 2017 The existence and stability results for a class of fractional differential equations involving generalized Katugampola derivative are presented herein. Some fixed point theorems are used and enlightening examples of obtained result are also given.
arxiv
A New Approach to Generalized Fractional Derivatives [PDF]
Bulletin of Mathematical Analysis and Applications, Vol 6, Issue
4, 2014, p.1-15, 2011 The author \mbox{(Appl. Math. Comput. 218(3):860-865, 2011)} introduced a new fractional integral operator given by, \[ \big({}^\rho \mathcal{I}^\alpha_{a+}f\big)(x) = \frac{\rho^{1- \alpha }}{\Gamma({\alpha})} \int^x_a \frac{\tau^{\rho-1} f(\tau) }{(x^\rho - \tau^\rho)^{1-\alpha}}\, d\tau, \] which generalizes the well-known Riemann-Liouville and the ...
arxiv
Applications of fractional calculus in solving Abel-type integral equations: Surface-volume reaction problem [PDF]
arXiv, 2015 In this paper we consider a class of partial integro-differential equations of fractional order, motivated by an equation which arises as a result of modeling surface-volume reactions in optical biosensors. We solve these equations by employing techniques from fractional calculus; several examples are discussed.
arxiv
A comprehensive review of the Pachpatte-type inequality pertaining to fractional integral operators [PDF]
Surveys in Mathematics and its ApplicationsIn the frame of fractional calculus, the term convexity is primarily utilized to address several challenges in both pure and applied research. The main focus and objective of this review paper is to present Pachpatte-type inequalities involving a variety
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