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  • 1.
    Mursaleen, Mohammad
    et al.
    Aligarh Muslim University, India.
    Pourhadi, Ehsan
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA). Iran University of Science and Technology, Iran.
    Saadati, Reza
    Iran University of Science and Technology, Iran.
    Solvability of infinite systems of second-order differential equations with boundary conditions in lp: Solvability of infinite systems2019Ingår i: Quaestiones Mathematicae. Journal of the South African Mathematical Society, ISSN 1607-3606, E-ISSN 1727-933X, s. 1-20Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, governed by the fundamental solutions we introduce the Green’s function of the second-order differential equations in general form with respect to boundary conditions and deal with the solvability of the infinite system of a second-order differential equations. Using the ideas of Hausdorff measure of noncompactness and Meir-Keleer condensing operator we seek the sufficient conditions to justify the existence of solutions for the aforementioned system in the Banach sequence space lp

  • 2.
    Pourhadi, Ehsan
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA). Iran University of Science and Technology, Iran.
    Some fixed point results are futile for the metric spaces with finite diameter2020Ingår i: Fixed Point Theory, ISSN 1583-5022, Vol. 21, nr 1, s. 305-308Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this short note, we state some crucial facts which have to be accompanied in a series of results in the literature. Furthermore, the aim of this paper is to warn researchers to be cautious in modeling different problems governed by expansive or contractive type mappings, in the setting of a bounded metric space

  • 3.
    Pourhadi, Ehsan
    et al.
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA). Iran University of Science and Technology, Iran.
    Khrennikov, Andrei
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    On the solutions of Cauchy problem for two classes of semi-linear pseudo-differential equations over p-adic field2018Ingår i: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 10, nr 4, s. 322-343Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Throughout this paper, using the p-adic wavelet basis together with the help of separation of variables and the Adomian decomposition method (as a scheme in numerical analysis) we initially investigate the solution of Cauchy problem for two classes of the first and second order of pseudo-differential equations involving the pseudo-differential operators such as Taibleson fractional operator in the setting of p-adic field.

  • 4.
    Pourhadi, Ehsan
    et al.
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Khrennikov, Andrei
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Saadati, Reza
    Iran University of Science and Technology, Iran.
    Oleschko, Klaudia
    Universidad Nacional Autonoma de Mexico (UNAM), Mexico.
    Correa Lopez, María de Jesús
    Edificio Piramide, Mexico.
    Solvability of the p-Adic Analogue of Navier–Stokes Equation via the Wavelet Theory2019Ingår i: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 21, nr 11, s. 1-20, artikel-id 1129Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    P-adic numbers serve as the simplest ultrametric model for the tree-like structures arisingin various physical and biological phenomena. Recently p-adic dynamical equations started to beapplied to geophysics, to model propagation of fluids (oil, water, and oil-in-water and water-in-oilemulsion) in capillary networks in porous random media. In particular, a p-adic analog of theNavier–Stokes equation was derived starting with a system of differential equations respectingthe hierarchic structure of a capillary tree. In this paper, using the Schauder fixed point theoremtogether with the wavelet functions, we extend the study of the solvability of a p-adic field analogof the Navier–Stokes equation derived from a system of hierarchic equations for fluid flow in acapillary network in porous medium. This equation describes propagation of fluid’s flow throughGeo-conduits, consisting of the mixture of fractures (as well as fracture’s corridors) and capillarynetworks, detected by seismic as joint wave/mass conducts. Furthermore, applying the Adomiandecomposition method we formulate the solution of the p-adic analog of the Navier–Stokes equationin term of series in general form. This solution may help researchers to come closer and find morefacts, taking into consideration the scaling, hierarchies, and formal derivations, imprinted from theanalogous aspects of the real world phenomena.

  • 5.
    Pourhadi, Ehsan
    et al.
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Saadati, Reza
    Iran Univ Sci & Technol, Iran.
    Kadelburg, Zoran
    Univ Belgrade, Serbia.
    Some Krasnosel'skii-type fixed point theorems for Meir-Keeler-type mappings2020Ingår i: Nonlinear Analysis: Modelling and Control, ISSN 1392-5113, E-ISSN 2335-8963, Vol. 25, nr 2, s. 257-265Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, inspired by the idea of Meir-Keeler contractive mappings, we introduce Meir-Keeler expansive mappings, say MKE, in order to obtain Krasnosel'skii-type fixed point theorems in Banach spaces. The idea of the paper is to combine the notion of Meir-Keeler mapping and expansive Krasnosel'skii fixed point theorem. We replace the expansion condition by the weakened MKE condition in some variants of Krasnosel'skii fixed point theorems that appear in the literature, e.g., in [T. Xiang, R. Yuan, A class of expansive-type Krasnosel'skii fixed point theorems, Nonlinear Anal., Theory Methods Appl., 71(7-8):3229-3239, 2009].

  • 6.
    Pourhadi, Ehsan
    et al.
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Saadati, Reza
    Iran University of Science and Technology, Iran.
    Kadelburg, Zoran
    University of Belgrade, Serbia.
    Some Krasnosel’skii-type fixed point theorems for Meir–Keeler-type mappings2020Ingår i: Nonlinear Analysis: Modelling and Control, ISSN 1392-5113, E-ISSN 2335-8963, Vol. 25, nr 2, s. 257-265Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, inspired by the idea of Meir–Keeler contractive mappings, we introduceMeir–Keeler expansive mappings, say MKE, in order to obtain Krasnosel’skii-type fixed pointtheorems in Banach spaces. The idea of the paper is to combine the notion of Meir–Keeler mappingand expansive Krasnosel’skii fixed point theorem. We replace the expansion condition by theweakened MKE condition in some variants of Krasnosel’skii fixed point theorems that appear inthe literature, e.g., in [T. Xiang, R. Yuan, A class of expansive-type Krasnosel’skii fixed pointtheorems, Nonlinear Anal., Theory Methods Appl., 71(7–8):3229–3239, 2009].

  • 7.
    Pourhadi, Ehsan
    et al.
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA). Iran University of Science and Technology, Iran.
    Saadati, Reza
    Iran University of Science and Technology, Iran.
    Ntouyas, Sotiris K.
    University of Ioannina, Greece;King Abdulaziz University, Saudi Arabia.
    Application of Fixed-Point Theory for a Nonlinear Fractional Three-Point Boundary-Value Problem2019Ingår i: Mathematics, E-ISSN 2227-7390, Vol. 7, nr 6, s. 1-11, artikel-id 526Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Throughout this paper, via the Schauder fixed-point theorem, a generalization of Krasnoselskii’s fixed-point theorem in a cone, as well as some inequalities relevant to Green’s function, we study the existence of positive solutions of a nonlinear, fractional three-point boundary-value problem with a term of the first order derivative [...]

  • 8.
    Saadati, R.
    et al.
    Iran Univ Sci & Technol, Iran.
    Pourhadi, Ehsan
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA). Iran Univ Sci & Technol, Iran.
    Samet, B.
    King Saud Univ, Saudi Arabia.
    On the PC-mild solutions of abstract fractional evolution equations with non-instantaneous impulses via the measure of noncompactness2019Ingår i: Boundary Value Problems, ISSN 1687-2762, E-ISSN 1687-2770, s. 1-23, artikel-id 19Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we deal with the existence results for mild solutions of abstract fractional evolution equations with non-instantaneous impulses on an unbounded interval. We also establish the existence of S-asymptotically -periodic mild solutions. The applied techniques are supported by the concept of measure of noncompactness in conjunction with the well-known Darbo-Sadovskii and Tichonov fixed-point theorems. Furthermore, an example to the fractional initial/boundary value Cauchy problem is concerned to illustrate our main results.

  • 9.
    Saadati, Reza
    et al.
    Iran University of Science and Technology, Iran.
    Pourhadi, Ehsan
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA). Iran University of Science and Technology, Iran.
    Mursaleen, Mohamad
    Aligarh Muslim University, India.
    Solvability of infinite systems of third-order differential equations in c0 by Meir-Keeler condensing operators2019Ingår i: Journal of Fixed Point Theory and Applications, ISSN 1661-7738, E-ISSN 1661-7746, Vol. 21, nr 2, s. 1-16, artikel-id 64Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Throughout this work, using the technique of measure of noncompactness together with Meir–Keeler condensing operators, we study the solvability of the following infinite system of third-order differential equations in the Banach sequence space c0 as a closed subspace of ℓ∞ :u′′′i+au′′i+bu′i+cui=fi(t,u1(t),u2(t),...)where fi∈C(R×R,R) is ω -periodic with respect to the first coordinate and a,b,c∈R are constant. Our approach depends on the Green's function corresponding to the aforesaid system and deduce some conclusions relevant to the existence of ω -periodic solutions in Banach sequence space c0 . In addition, some examples are supplied to illustrate the usefulness of the outcome.

    Publikationen är tillgänglig i fulltext från 2020-05-04 09:06
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